The Improved Arithmetic-Geometric Mean Inequalities for Matrix Norms
|
|
- Simon Francis
- 5 years ago
- Views:
Transcription
1 Applied Mathematical Sciences, Vol 7, 03, no 9, HIKARI Ltd, wwwm-hikaricom The Improved Arithmetic-Geometric Mean Inequalities for Matrix Norms I Halil Gumus Adıyaman University, Faculty of Arts and Sciences Department of Mathematics, 0040, Adıyaman, Turkey gumusibo@hotmailcom Necati Taskara Selcuk University, Science Faculty Department of Mathematics 4075, Kampus, Konya, Turkey ntaskara@selcukedutr Copyright c 03 I Halil Gumus and Necati Taskara This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited Abstract In this paper, we prove a scalar inequality such that this inequality is an improvement of the classical arithmetic-geometric mean inequality We obtain its matrix version and investigate Hilbert-Schmidt and trace norm of this matrix version Mathematics Subject Classification: 5A45; 5A60 Keywords: Positive semidefinite matrix, Unitarily invariant norm, arithmeticgeometric mean inequality Introduction Let M n (C be the space of all n n complex matrices For Hermitian matrices A,B M n (C, we write A B to mean A B is positive semidefinite,
2 440 I Halil Gumus and N Taskara particularly, A 0 indicates that A is positive semidefinite Let denote unitarily invariant norm on M n (C So, for all A M n (C and all unitary matrices U,V M n (C, we can write UAV A ( If A [a ij ] M n (C, then the Hilbert-Schmidt norm of A is given by A ( i, a ij ( and the trace norm of A is given by A s j (A tr A, (3 where s (A s n (A are the singular values of A, that is, the eigenvalues of the positive semidefinite matrix A (A A It is known that these norms are unitarily invariant The Young inequality says that if a, b 0 and 0 v, then a v b v va +( vb Specifically, for a b, the above inequality turns into the equality If v, then we obtain the arithmetic-geometric mean inequality ab a + b (4 In [5], for A, B, X M n (C such that A and B are positive semidefinite, Kosaki proved that A v XB v vax +( vxb, where 0 v In [4], for a, b 0 and 0 v, Manasrah and Kittaneh proved that a v b v + r 0 ( a b va +( vb, (5 where r 0 min{v, v} Also, by using (5, they showed that A v B v + r 0 ( A B va +( vb
3 Arithmetic-geometric mean inequalities 44 In [3], for a, b 0 and p, q > with + p q proved that, Hirzallah and Kittaneh ( a p p + bq q r (ap b q + a b By using this inequality, for A, B are positive semidefinite matrices, they obtained that p Ap X + q XBq r Ap X XB q + AXB, where r max(p, q In [], for A, B M n (C such that A, B are positive definite and A B, we proved that 8 s j ( A (A B A s j ( A + B A# B ( 8 s j B (A B B for j,,, n, where A# B is the geometric mean of A and B and s j (X,are the singular values of an n n matrix X for j,,, n In this study, we give a scalar inequality such that this inequality is an improvement of (4 Then we write its matrix version and prove its trace norm inequality By rearranging this scalar inequality, we obtain the Hilbert- Schmidt norm inequality for its matrix version Main Results The following inequality was given by Mitrinovic in [6]: (a b 8 a a + b ab (a b (6 8 b It is easily seen that the left side of this inequality is an improvement of (4 In (6, if we take m,n R + such that a m, b n and m n>0, then we get (m n m + n mn (m n 8 m 8 n If we refine this inequality, then we have (m n (m n (m n 4 m 4 n
4 44 I Halil Gumus and N Taskara Then, we can generalize this inequality for k natural numbers as ( m k+ n k+ ( ( m k n k m k+ n k+ 4 m 4 n Now, in the following lemmas and theorems, we give the proof of the above scalar inequalities and obtain their matrix norm inequalities Lemma If a b>0, then we have (a b 8 a a + b ab (a b 8 b Proof Firstly, let s prove the left side of inequality If b a, then we have b +a a By multiplying both sides of this inequality with a b, we get a b a a b If we take the square of both sides and rearrange this inequality, it is obtained (a b 8 a a + b ab Now, we prove the right side of the inequality If b a, then we get b a Hence we can write b b + a Similarly we have as required a + b ab (a b 8 b Lemma [] Let A, B M n (CThen s j (AB s j (As j (B (7 Theorem 3 For A B>0, we can write the following inequality s j(a+ s j(b A B + A B A + B 8 A Proof By using the left side of Lemma, we can write (s j (A s j (B 8 s j (A + s j (As j (B s j(a+s j (B, (8
5 Arithmetic-geometric mean inequalities 443 where j,,, n From (3 and (8, we have A + B tr(a + B s j (As j (B+ 8 s j (A+s j (B s j(a s j (As j (B+s j(b s j (A s j (A sj (B + s j(a+ s j(b 8 s j(a s j(as j (B By considering Cauchy-Schwarz inequality and (7, we obtain A + B s j (A B + 8 A B + 8 Therefore we have the required inequality s j (A+ s j (B ( n s j(a( n s j(b tra s j (A+ s j (B A B A Theorem 4 For A B>0, we have s j (A+ s j (B A B + A B A + B 8 B Proof By the same operations, the proof is easily checked Lemma 5 For m n>0 and k natural numbers, we can write (m k+ n k+ ( m k n k (m k+ n k+ 4 m 4 n Proof We prove the left side of this inequality with mathematical induction method For k, we show that the inequality is true It is clear that m+n If m this inequality is multiplied with conjugate of m + n, then we have ( m n (m n m Assume that it is true for all positive integers a, that is, m a+ n a+ m a n a m
6 444 I Halil Gumus and N Taskara If we refine this inequality, then we get n a+ mn a m a+ Hence we have to show that it is true for a + Then, for m n>0, we have n a+ nm a+ mn a+ mm a+ mn a+ m a+ mn a+ If it is arranged by adding m + to both side of inequality, we obtain m a+ n a+ m a+ mn a+ m a+ n a+ m a+ n a+ m ( m a+ n a+ ( m a+ n a+ m which ends up the induction Also, the proof of rigth side can be seen by using the same method Theorem 6 Let A, B M n (C be positive semidefinite matricesif all eigenvalues of A are bigger than all eigenvalues of B, then we get A (A k+ X XB k+ 4 ( A k X XB k A k+ X XB k+ B 4 Proof Let s prove the left side of the inequality Since every positive semidefinite matrix is unitarily diagonalizable, it is seen that there are unitary matrices U, V M n (C such that A UλU and B VMV, where λ diag(λ,λ,, λ n,m diag(μ,μ,, μ n and all λ i,μ i are nonnegative If Y U XV [y ij ], then we have 4 A (A k+ X XB k+ 4 Uλ U (Uλ k+ U UY V UY V VM k+ V 4 Uλ U (Uλ k+ YV UY M k+ V 4 Uλ (λ k+ Y YM k+ V U( λk+ i μ k+ j 4λ i y ij V
7 Arithmetic-geometric mean inequalities 445 Similarly, we have A k X XB k Uλ k U UY V UY V VM k V U(λ k Y YM k V U( ( λ k i μk j yij V By using (, ( and applying Lemma 5 to the nonnegative numbers λ i,μ j for i,, n, we obtain A (A k+ X XB k+ 4 i, i, ( λk+ i μ k+ j y ij λ i ( λ k i μk j yij A k X XB k Thus, this completes the proof of the left side Similarly, we show the right side of theorem We have 4 (Ak+ X XB k+ B 4 (Uλk+ U UY V UY V VM k+ V VM V 4 (Uλk+ YV UY M k+ V VM V 4 U(λk+ Y YM k+ M V U( λk+ i μ k+ j y ij V 4μ i Also, we write AX XB i, i, ( λ k i μ k j yij ( λk+ i μ k+ j μ i y ij ( A k+ X XB k+ B 4 and so the proof of theorem is completed References [] Bhatia, R: Matrix Analysis Springer-Verlag 997 [] Gumus, IH, Hirzallah, O, Taskara, N: Singular value inequalities for the arithmetic, geometric and Heinz means of matrices Linear and Multilinear Algebra Vol 59, No, (0
8 446 I Halil Gumus and N Taskara [3] Hirzallah, O, Kittaneh, F: Matrix Young inequalities for the Hilbert- Schmidt norm Linear Algebra Appl 308, (000 [4] Kittaneh, F, Manasrah Y: Improved Young and Heinz inequalities for matrices Journal of Mathematical Analysis and Applications 36, 6-69 (00 [5] Kosaki, H: Arithmetic geometric mean and related inequalities for operators J Funct Anal 56, (998 [6] Mitrinovic, DS: Analytic Inequalities New York Springer Verlag 970 Received: January, 03
Some inequalities for unitarily invariant norms of matrices
Wang et al Journal of Inequalities and Applications 011, 011:10 http://wwwjournalofinequalitiesandapplicationscom/content/011/1/10 RESEARCH Open Access Some inequalities for unitarily invariant norms of
More informationarxiv: v1 [math.fa] 19 Aug 2017
EXTENSIONS OF INTERPOLATION BETWEEN THE ARITHMETIC-GEOMETRIC MEAN INEQUALITY FOR MATRICES M. BAKHERAD 1, R. LASHKARIPOUR AND M. HAJMOHAMADI 3 arxiv:1708.0586v1 [math.fa] 19 Aug 017 Abstract. In this paper,
More informationExtensions of interpolation between the arithmetic-geometric mean inequality for matrices
Bakherad et al. Journal of Inequalities and Applications 017) 017:09 DOI 10.1186/s13660-017-1485-x R E S E A R C H Open Access Extensions of interpolation between the arithmetic-geometric mean inequality
More informationThe matrix arithmetic-geometric mean inequality revisited
isid/ms/007/11 November 1 007 http://wwwisidacin/ statmath/eprints The matrix arithmetic-geometric mean inequality revisited Rajendra Bhatia Fuad Kittaneh Indian Statistical Institute Delhi Centre 7 SJSS
More informationarxiv: v1 [math.fa] 1 Oct 2015
SOME RESULTS ON SINGULAR VALUE INEQUALITIES OF COMPACT OPERATORS IN HILBERT SPACE arxiv:1510.00114v1 math.fa 1 Oct 2015 A. TAGHAVI, V. DARVISH, H. M. NAZARI, S. S. DRAGOMIR Abstract. We prove several singular
More informationSingular Value and Norm Inequalities Associated with 2 x 2 Positive Semidefinite Block Matrices
Electronic Journal of Linear Algebra Volume 32 Volume 32 (2017) Article 8 2017 Singular Value Norm Inequalities Associated with 2 x 2 Positive Semidefinite Block Matrices Aliaa Burqan Zarqa University,
More informationNotes on matrix arithmetic geometric mean inequalities
Linear Algebra and its Applications 308 (000) 03 11 www.elsevier.com/locate/laa Notes on matrix arithmetic geometric mean inequalities Rajendra Bhatia a,, Fuad Kittaneh b a Indian Statistical Institute,
More informationAbstract. In this article, several matrix norm inequalities are proved by making use of the Hiroshima 2003 result on majorization relations.
HIROSHIMA S THEOREM AND MATRIX NORM INEQUALITIES MINGHUA LIN AND HENRY WOLKOWICZ Abstract. In this article, several matrix norm inequalities are proved by making use of the Hiroshima 2003 result on majorization
More informationTrace Inequalities for a Block Hadamard Product
Filomat 32:1 2018), 285 292 https://doiorg/102298/fil1801285p Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://wwwpmfniacrs/filomat Trace Inequalities for
More informationSolving Homogeneous Systems with Sub-matrices
Pure Mathematical Sciences, Vol 7, 218, no 1, 11-18 HIKARI Ltd, wwwm-hikaricom https://doiorg/112988/pms218843 Solving Homogeneous Systems with Sub-matrices Massoud Malek Mathematics, California State
More informationA Note on Product Range of 3-by-3 Normal Matrices
International Mathematical Forum, Vol. 11, 2016, no. 18, 885-891 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2016.6796 A Note on Product Range of 3-by-3 Normal Matrices Peng-Ruei Huang
More informationNorm inequalities related to the Heinz means
Gao and Ma Journal of Inequalities and Applications (08) 08:303 https://doi.org/0.86/s3660-08-89-7 R E S E A R C H Open Access Norm inequalities related to the Heinz means Fugen Gao * and Xuedi Ma * Correspondence:
More informationIMPROVED ARITHMETIC-GEOMETRIC AND HEINZ MEANS INEQUALITIES FOR HILBERT SPACE OPERATORS
IMPROVED ARITHMETI-GEOMETRI AND HEINZ MEANS INEQUALITIES FOR HILBERT SPAE OPERATORS FUAD KITTANEH, MARIO KRNIĆ, NEDA LOVRIČEVIĆ, AND JOSIP PEČARIĆ Abstract. The main objective of this paper is an improvement
More informationNorm inequalities related to the matrix geometric mean
isid/ms/2012/07 April 20, 2012 http://www.isid.ac.in/ statmath/eprints Norm inequalities related to the matrix geometric mean RAJENDRA BHATIA PRIYANKA GROVER Indian Statistical Institute, Delhi Centre
More informationGeneralized Numerical Radius Inequalities for Operator Matrices
International Mathematical Forum, Vol. 6, 011, no. 48, 379-385 Generalized Numerical Radius Inequalities for Operator Matrices Wathiq Bani-Domi Department of Mathematics Yarmouk University, Irbed, Jordan
More informationA Numerical Radius Version of the Arithmetic-Geometric Mean of Operators
Filomat 30:8 (2016), 2139 2145 DOI 102298/FIL1608139S Published by Faculty of Sciences and Mathematics, University of Niš, Serbia vailable at: htt://wwwmfniacrs/filomat Numerical Radius Version of the
More informationInterpolating the arithmetic geometric mean inequality and its operator version
Linear Algebra and its Applications 413 (006) 355 363 www.elsevier.com/locate/laa Interpolating the arithmetic geometric mean inequality and its operator version Rajendra Bhatia Indian Statistical Institute,
More informationk-pell, k-pell-lucas and Modified k-pell Numbers: Some Identities and Norms of Hankel Matrices
International Journal of Mathematical Analysis Vol. 9, 05, no., 3-37 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.4370 k-pell, k-pell-lucas and Modified k-pell Numbers: Some Identities
More informationSINGULAR VALUE INEQUALITIES FOR COMPACT OPERATORS
SINGULAR VALUE INEQUALITIES FOR OMPAT OPERATORS WASIM AUDEH AND FUAD KITTANEH Abstract. A singular value inequality due to hatia and Kittaneh says that if A and are compact operators on a complex separable
More informationSingular Value Inequalities for Real and Imaginary Parts of Matrices
Filomat 3:1 16, 63 69 DOI 1.98/FIL16163C Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Singular Value Inequalities for Real Imaginary
More informationInequalities involving eigenvalues for difference of operator means
Electronic Journal of Linear Algebra Volume 7 Article 5 014 Inequalities involving eigenvalues for difference of operator means Mandeep Singh msrawla@yahoo.com Follow this and additional works at: http://repository.uwyo.edu/ela
More informationRecurrence Relations between Symmetric Polynomials of n-th Order
Applied Mathematical Sciences, Vol. 8, 214, no. 15, 5195-522 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.214.47525 Recurrence Relations between Symmetric Polynomials of n-th Order Yuriy
More informationRemarks on Fuglede-Putnam Theorem for Normal Operators Modulo the Hilbert-Schmidt Class
International Mathematical Forum, Vol. 9, 2014, no. 29, 1389-1396 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.47141 Remarks on Fuglede-Putnam Theorem for Normal Operators Modulo the
More informationarxiv: v4 [math.sp] 19 Jun 2015
arxiv:4.0333v4 [math.sp] 9 Jun 205 An arithmetic-geometric mean inequality for products of three matrices Arie Israel, Felix Krahmer, and Rachel Ward June 22, 205 Abstract Consider the following noncommutative
More informationOn the Generalized Reid Inequality and the Numerical Radii
Applied Mathematical Sciences, Vol. 5, 2011, no. 9, 441-445 On the Generalized Reid Inequality and the Numerical Radii J. O. Bonyo 1, D. O. Adicka 2, J. O. Agure 3 1,3 Department of Mathematics and Applied
More informationSome Range-Kernel Orthogonality Results for Generalized Derivation
International Journal of Contemporary Mathematical Sciences Vol. 13, 2018, no. 3, 125-131 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2018.8412 Some Range-Kernel Orthogonality Results for
More informationGENERALIZED NORMS INEQUALITIES FOR ABSOLUTE VALUE OPERATORS
International Journal of Analysis Alications ISSN 9-8639 Volume 5, Number (04), -9 htt://www.etamaths.com GENERALIZED NORMS INEQUALITIES FOR ABSOLUTE VALUE OPERATORS ILYAS ALI, HU YANG, ABDUL SHAKOOR Abstract.
More informationMath 489AB Exercises for Chapter 2 Fall Section 2.3
Math 489AB Exercises for Chapter 2 Fall 2008 Section 2.3 2.3.3. Let A M n (R). Then the eigenvalues of A are the roots of the characteristic polynomial p A (t). Since A is real, p A (t) is a polynomial
More informationOn a Boundary-Value Problem for Third Order Operator-Differential Equations on a Finite Interval
Applied Mathematical Sciences, Vol. 1, 216, no. 11, 543-548 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.216.512743 On a Boundary-Value Problem for Third Order Operator-Differential Equations
More informationarxiv: v1 [math.fa] 6 Nov 2015
CARTESIAN DECOMPOSITION AND NUMERICAL RADIUS INEQUALITIES FUAD KITTANEH, MOHAMMAD SAL MOSLEHIAN AND TAKEAKI YAMAZAKI 3 arxiv:5.0094v [math.fa] 6 Nov 05 Abstract. We show that if T = H + ik is the Cartesian
More informationConvex Sets Strict Separation in Hilbert Spaces
Applied Mathematical Sciences, Vol. 8, 2014, no. 64, 3155-3160 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.44257 Convex Sets Strict Separation in Hilbert Spaces M. A. M. Ferreira 1
More informationSums of Tribonacci and Tribonacci-Lucas Numbers
International Journal of Mathematical Analysis Vol. 1, 018, no. 1, 19-4 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.018.71153 Sums of Tribonacci Tribonacci-Lucas Numbers Robert Frontczak
More informationClarkson Inequalities With Several Operators
isid/ms/2003/23 August 14, 2003 http://www.isid.ac.in/ statmath/eprints Clarkson Inequalities With Several Operators Rajendra Bhatia Fuad Kittaneh Indian Statistical Institute, Delhi Centre 7, SJSS Marg,
More informationRiesz Representation Theorem on Generalized n-inner Product Spaces
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 18, 873-882 HIKARI Ltd, www.m-hikari.com Riesz Representation Theorem on Generalized n-inner Product Spaces Pudji Astuti Faculty of Mathematics and Natural
More informationarxiv: v1 [math.fa] 12 Oct 2016
UNITARILY INVARIANT NORM INEQUALITIES FOR ELEMENTARY OPERATORS INVOLVING G 1 OPERATORS FUAD KITTANEH, MOHAMMAD SAL MOSLEHIAN, AND MOHAMMAD SABABHEH arxiv:161.3869v1 [math.fa] 1 Oct 16 Abstract. In this
More informationElementary linear algebra
Chapter 1 Elementary linear algebra 1.1 Vector spaces Vector spaces owe their importance to the fact that so many models arising in the solutions of specific problems turn out to be vector spaces. The
More informationOn the Characterization Feedback of Positive LTI Continuous Singular Systems of Index 1
Advanced Studies in Theoretical Physics Vol. 8, 2014, no. 27, 1185-1190 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2014.48245 On the Characterization Feedback of Positive LTI Continuous
More informationON THE HÖLDER CONTINUITY OF MATRIX FUNCTIONS FOR NORMAL MATRICES
Volume 10 (2009), Issue 4, Article 91, 5 pp. ON THE HÖLDER CONTINUITY O MATRIX UNCTIONS OR NORMAL MATRICES THOMAS P. WIHLER MATHEMATICS INSTITUTE UNIVERSITY O BERN SIDLERSTRASSE 5, CH-3012 BERN SWITZERLAND.
More informationHyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation on a Restricted Domain
Int. Journal of Math. Analysis, Vol. 7, 013, no. 55, 745-75 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.013.394 Hyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation
More informationMatrix Inequalities by Means of Block Matrices 1
Mathematical Inequalities & Applications, Vol. 4, No. 4, 200, pp. 48-490. Matrix Inequalities by Means of Block Matrices Fuzhen Zhang 2 Department of Math, Science and Technology Nova Southeastern University,
More informationPermanents and Determinants of Tridiagonal Matrices with (s, t)-pell Numbers
International Mathematical Forum, Vol 12, 2017, no 16, 747-753 HIKARI Ltd, wwwm-hikaricom https://doiorg/1012988/imf20177652 Permanents and Determinants of Tridiagonal Matrices with (s, t)-pell Numbers
More informationSome Inequalities for Commutators of Bounded Linear Operators in Hilbert Spaces
Some Inequalities for Commutators of Bounded Linear Operators in Hilbert Spaces S.S. Dragomir Abstract. Some new inequalities for commutators that complement and in some instances improve recent results
More informationOn a Certain Representation in the Pairs of Normed Spaces
Applied Mathematical Sciences, Vol. 12, 2018, no. 3, 115-119 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.712362 On a Certain Representation in the Pairs of ormed Spaces Ahiro Hoshida
More informationA Note of the Strong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 10, 2016, no. 6, 255-261 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.511700 A Note of the Strong Convergence of the Mann Iteration for Demicontractive
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics MATRIX AND OPERATOR INEQUALITIES FOZI M DANNAN Department of Mathematics Faculty of Science Qatar University Doha - Qatar EMail: fmdannan@queduqa
More informationA Disaggregation Approach for Solving Linear Diophantine Equations 1
Applied Mathematical Sciences, Vol. 12, 2018, no. 18, 871-878 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.8687 A Disaggregation Approach for Solving Linear Diophantine Equations 1 Baiyi
More informationLecture 5. Ch. 5, Norms for vectors and matrices. Norms for vectors and matrices Why?
KTH ROYAL INSTITUTE OF TECHNOLOGY Norms for vectors and matrices Why? Lecture 5 Ch. 5, Norms for vectors and matrices Emil Björnson/Magnus Jansson/Mats Bengtsson April 27, 2016 Problem: Measure size of
More informationSecond Proof: Every Positive Integer is a Frobenius Number of Three Generators
International Mathematical Forum, Vol., 5, no. 5, - 7 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.988/imf.5.54 Second Proof: Ever Positive Integer is a Frobenius Number of Three Generators Firu Kamalov
More informationof a Two-Operator Product 1
Applied Mathematical Sciences, Vol. 7, 2013, no. 130, 6465-6474 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.39501 Reverse Order Law for {1, 3}-Inverse of a Two-Operator Product 1 XUE
More information2. reverse inequalities via specht ratio To study the Golden-Thompson inequality, Ando-Hiai in [1] developed the following log-majorizationes:
ON REVERSES OF THE GOLDEN-THOMPSON TYPE INEQUALITIES MOHAMMAD BAGHER GHAEMI, VENUS KALEIBARY AND SHIGERU FURUICHI arxiv:1708.05951v1 [math.fa] 20 Aug 2017 Abstract. In this paper we present some reverses
More informationPERTURBATION ANAYSIS FOR THE MATRIX EQUATION X = I A X 1 A + B X 1 B. Hosoo Lee
Korean J. Math. 22 (214), No. 1, pp. 123 131 http://dx.doi.org/1.11568/jm.214.22.1.123 PERTRBATION ANAYSIS FOR THE MATRIX EQATION X = I A X 1 A + B X 1 B Hosoo Lee Abstract. The purpose of this paper is
More informationEE/ACM Applications of Convex Optimization in Signal Processing and Communications Lecture 2
EE/ACM 150 - Applications of Convex Optimization in Signal Processing and Communications Lecture 2 Andre Tkacenko Signal Processing Research Group Jet Propulsion Laboratory April 5, 2012 Andre Tkacenko
More information2-Semi-Norms and 2*-Semi-Inner Product
International Journal of Mathematical Analysis Vol. 8, 01, no. 5, 601-609 HIKARI Ltd, www.m-hiari.com http://dx.doi.org/10.1988/ima.01.103 -Semi-Norms and *-Semi-Inner Product Samoil Malčesi Centre for
More informationInequalities For Singular Values And Traces Of Quaternion Hermitian Matrices
Inequalities For Singular Values And Traces Of Quaternion Hermitian Matrices K. Gunasekaran M. Rahamathunisha Ramanujan Research Centre, PG and Research Department of Mathematics, Government Arts College
More informationSome inequalities for sum and product of positive semide nite matrices
Linear Algebra and its Applications 293 (1999) 39±49 www.elsevier.com/locate/laa Some inequalities for sum and product of positive semide nite matrices Bo-Ying Wang a,1,2, Bo-Yan Xi a, Fuzhen Zhang b,
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationSeveral Applications of Young-Type and Holder s Inequalities
Applied Mathematical Sciences, Vol. 0, 06, no. 36, 763-774 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ams.06.675 Several Applications of Young-Type and Holder s Ineualities Loredana Ciurdariu
More informationOn Powers of General Tridiagonal Matrices
Applied Mathematical Sciences, Vol. 9, 5, no., 583-59 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.988/ams.5.49 On Powers of General Tridiagonal Matrices Qassem M. Al-Hassan Department of Mathematics
More informationDetection Whether a Monoid of the Form N n / M is Affine or Not
International Journal of Algebra Vol 10 2016 no 7 313-325 HIKARI Ltd wwwm-hikaricom http://dxdoiorg/1012988/ija20166637 Detection Whether a Monoid of the Form N n / M is Affine or Not Belgin Özer and Ece
More informationSOME INEQUALITIES FOR COMMUTATORS OF BOUNDED LINEAR OPERATORS IN HILBERT SPACES. S. S. Dragomir
Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 5: 011), 151 16 DOI: 10.98/FIL110151D SOME INEQUALITIES FOR COMMUTATORS OF BOUNDED LINEAR
More informationOn Positive Stable Realization for Continuous Linear Singular Systems
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 8, 395-400 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4246 On Positive Stable Realization for Continuous Linear Singular Systems
More informationA Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating Polynomials
Applied Mathematical Sciences, Vol. 8, 2014, no. 35, 1723-1730 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.4127 A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating
More informationβ Baire Spaces and β Baire Property
International Journal of Contemporary Mathematical Sciences Vol. 11, 2016, no. 5, 211-216 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2016.612 β Baire Spaces and β Baire Property Tugba
More informationOn the Laplacian Energy of Windmill Graph. and Graph D m,cn
International Journal of Contemporary Mathematical Sciences Vol. 11, 2016, no. 9, 405-414 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2016.6844 On the Laplacian Energy of Windmill Graph
More informationEquivalent Multivariate Stochastic Processes
International Journal of Mathematical Analysis Vol 11, 017, no 1, 39-54 HIKARI Ltd, wwwm-hikaricom https://doiorg/101988/ijma01769111 Equivalent Multivariate Stochastic Processes Arnaldo De La Barrera
More informationResearch Article A Note on Kantorovich Inequality for Hermite Matrices
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 0, Article ID 5767, 6 pages doi:0.55/0/5767 Research Article A Note on Kantorovich Inequality for Hermite Matrices Zhibing
More informationDiophantine Equations. Elementary Methods
International Mathematical Forum, Vol. 12, 2017, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.7223 Diophantine Equations. Elementary Methods Rafael Jakimczuk División Matemática,
More informationL p Theory for the div-curl System
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 6, 259-271 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4112 L p Theory for the div-curl System Junichi Aramaki Division of Science,
More informationOn Symmetric Bi-Multipliers of Lattice Implication Algebras
International Mathematical Forum, Vol. 13, 2018, no. 7, 343-350 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2018.8423 On Symmetric Bi-Multipliers of Lattice Implication Algebras Kyung Ho
More informationPAijpam.eu ON THE BOUNDS FOR THE NORMS OF R-CIRCULANT MATRICES WITH THE JACOBSTHAL AND JACOBSTHAL LUCAS NUMBERS Ş. Uygun 1, S.
International Journal of Pure and Applied Mathematics Volume 11 No 1 017, 3-10 ISSN: 1311-8080 (printed version); ISSN: 1314-335 (on-line version) url: http://wwwijpameu doi: 10173/ijpamv11i17 PAijpameu
More informationBoundary Value Problem for Second Order Ordinary Linear Differential Equations with Variable Coefficients
International Journal of Mathematical Analysis Vol. 9, 2015, no. 3, 111-116 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.12988/ijma.2015.411353 Boundary Value Problem for Second Order Ordinary Linear
More informationOn a Diophantine Equation 1
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 2, 73-81 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.728 On a Diophantine Equation 1 Xin Zhang Department
More informationLinear Algebra Massoud Malek
CSUEB Linear Algebra Massoud Malek Inner Product and Normed Space In all that follows, the n n identity matrix is denoted by I n, the n n zero matrix by Z n, and the zero vector by θ n An inner product
More informationTrace inequalities for positive semidefinite matrices with centrosymmetric structure
Zhao et al Journal of Inequalities pplications 1, 1:6 http://wwwjournalofinequalitiesapplicationscom/content/1/1/6 RESERCH Trace inequalities for positive semidefinite matrices with centrosymmetric structure
More informationBounds Improvement for Neuman-Sándor Mean Using Arithmetic, Quadratic and Contraharmonic Means 1
International Mathematical Forum, Vol. 8, 2013, no. 30, 1477-1485 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.36125 Bounds Improvement for Neuman-Sándor Mean Using Arithmetic, Quadratic
More informationChapter 6 Inner product spaces
Chapter 6 Inner product spaces 6.1 Inner products and norms Definition 1 Let V be a vector space over F. An inner product on V is a function, : V V F such that the following conditions hold. x+z,y = x,y
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. 6 (2012), no. 1, 139 146 Banach Journal of Mathematical Analysis ISSN: 1735-8787 (electronic) www.emis.de/journals/bjma/ AN EXTENSION OF KY FAN S DOMINANCE THEOREM RAHIM ALIZADEH
More informationA Fixed Point Approach to the Stability of a Quadratic-Additive Type Functional Equation in Non-Archimedean Normed Spaces
International Journal of Mathematical Analysis Vol. 9, 015, no. 30, 1477-1487 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.1988/ijma.015.53100 A Fied Point Approach to the Stability of a Quadratic-Additive
More informationThe singular value of A + B and αa + βb
An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, 2016, f. 2, vol. 3 The singular value of A + B and αa + βb Bogdan D. Djordjević Received: 16.II.2015 / Revised: 3.IV.2015 / Accepted: 9.IV.2015
More informationSingular Value Inequalities for Compact Normal Operators
dvance in Linear lgebra & Matrix Theory, 3, 3, 34-38 Publihed Online December 3 (http://www.cirp.org/ournal/alamt) http://dx.doi.org/.436/alamt.3.347 Singular Value Inequalitie for Compact Normal Operator
More informationA Family of Nonnegative Matrices with Prescribed Spectrum and Elementary Divisors 1
International Mathematical Forum, Vol, 06, no 3, 599-63 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/0988/imf0668 A Family of Nonnegative Matrices with Prescribed Spectrum and Elementary Divisors Ricardo
More informationk-jacobsthal and k-jacobsthal Lucas Matrix Sequences
International Mathematical Forum, Vol 11, 016, no 3, 145-154 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/imf0165119 k-jacobsthal and k-jacobsthal Lucas Matrix Sequences S Uygun 1 and H Eldogan Department
More informationOn the Power of Standard Polynomial to M a,b (E)
International Journal of Algebra, Vol. 10, 2016, no. 4, 171-177 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.6214 On the Power of Standard Polynomial to M a,b (E) Fernanda G. de Paula
More informationOn a decomposition lemma for positive semi-definite block-matrices
On a decomposition lemma for positive semi-definite bloc-matrices arxiv:10.0473v1 [math.fa] Feb 01 Jean-Christophe ourin, Eun-Young Lee, Minghua Lin January, 01 Abstract This short note, in part of expository
More informationCaristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces
International Journal of Mathematical Analysis Vol. 11, 2017, no. 6, 267-275 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.717 Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric
More informationLeft R-prime (R, S)-submodules
International Mathematical Forum, Vol. 8, 2013, no. 13, 619-626 HIKARI Ltd, www.m-hikari.com Left R-prime (R, S)-submodules T. Khumprapussorn Department of Mathematics, Faculty of Science King Mongkut
More informationSurjective Maps Preserving Local Spectral Radius
International Mathematical Forum, Vol. 9, 2014, no. 11, 515-522 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.414 Surjective Maps Preserving Local Spectral Radius Mustapha Ech-Cherif
More informationRefinement of Steffensen s Inequality for Superquadratic functions
Int. Journal of Math. Analysis, Vol. 8, 14, no. 13, 611-617 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.1988/ijma.14.45 Refinement of Steffensen s Inequality for Superquadratic functions Mohammed
More informationGroup Inverse for a Class of. Centrosymmetric Matrix
International athematical Forum, Vol. 13, 018, no. 8, 351-356 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/imf.018.8530 Group Inverse for a Class of Centrosymmetric atrix ei Wang and Junqing Wang
More informationSequences from Heptagonal Pyramid Corners of Integer
International Mathematical Forum, Vol 13, 2018, no 4, 193-200 HIKARI Ltd, wwwm-hikaricom https://doiorg/1012988/imf2018815 Sequences from Heptagonal Pyramid Corners of Integer Nurul Hilda Syani Putri,
More informationInner products and Norms. Inner product of 2 vectors. Inner product of 2 vectors x and y in R n : x 1 y 1 + x 2 y x n y n in R n
Inner products and Norms Inner product of 2 vectors Inner product of 2 vectors x and y in R n : x 1 y 1 + x 2 y 2 + + x n y n in R n Notation: (x, y) or y T x For complex vectors (x, y) = x 1 ȳ 1 + x 2
More information1 Linear Algebra Problems
Linear Algebra Problems. Let A be the conjugate transpose of the complex matrix A; i.e., A = A t : A is said to be Hermitian if A = A; real symmetric if A is real and A t = A; skew-hermitian if A = A and
More informationLocal Extreme Points and a Young-Type Inequality
Alied Mathematical Sciences Vol. 08 no. 6 65-75 HIKARI Ltd www.m-hikari.com htts://doi.org/0.988/ams.08.886 Local Extreme Points a Young-Te Inequalit Loredana Ciurdariu Deartment of Mathematics Politehnica
More informationFixed Point Theorems for Modular Contraction Mappings on Modulared Spaces
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 20, 965-972 HIKARI Ltd, www.m-hikari.com Fixed Point Theorems for Modular Contraction Mappings on Modulared Spaces Mariatul Kiftiah Dept. of Math., Tanjungpura
More informationThe Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces
Applied Mathematical Sciences, Vol. 11, 2017, no. 12, 549-560 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.718 The Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive
More informationThe Ruled Surfaces According to Type-2 Bishop Frame in E 3
International Mathematical Forum, Vol. 1, 017, no. 3, 133-143 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/imf.017.610131 The Ruled Surfaces According to Type- Bishop Frame in E 3 Esra Damar Department
More informationLecture Notes 1: Vector spaces
Optimization-based data analysis Fall 2017 Lecture Notes 1: Vector spaces In this chapter we review certain basic concepts of linear algebra, highlighting their application to signal processing. 1 Vector
More informationInequalities for Modules and Unitary Invariant Norms
Int. J. Contemp. Math. Sciences Vol. 7 202 no. 36 77-783 Inequalities for Modules and Unitary Invariant Norms Loredana Ciurdariu Department of Mathematics Politehnica University of Timisoara P-ta. Victoriei
More informationCompound matrices and some classical inequalities
Compound matrices and some classical inequalities Tin-Yau Tam Mathematics & Statistics Auburn University Dec. 3, 04 We discuss some elegant proofs of several classical inequalities of matrices by using
More informationDouble Total Domination on Generalized Petersen Graphs 1
Applied Mathematical Sciences, Vol. 11, 2017, no. 19, 905-912 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.7114 Double Total Domination on Generalized Petersen Graphs 1 Chengye Zhao 2
More information