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Titolo:
TRACE AND EIGENVALUE INEQUALITIES FOR ORDINARY AND HADAMARD-PRODUCTS OF POSITIVE SEMIDEFINITE HERMITIAN MATRICES
Autore:
WANG BY; ZHANG FZ;
Indirizzi:
BEIJING NORMAL UNIV,DEPT MATH BEIJING 100875 PEOPLES R CHINA NOVA SOUTHEASTERN UNIV,DEPT MATH FT LAUDERDALE FL 33314
Titolo Testata:
SIAM journal on matrix analysis and applications
fascicolo: 4, volume: 16, anno: 1995,
pagine: 1173 - 1183
SICI:
0895-4798(1995)16:4<1173:TAEIFO>2.0.ZU;2-I
Fonte:
ISI
Lingua:
ENG
Soggetto:
POWER PRODUCTS;
Keywords:
TRACE INEQUALITY; EIGENVALUE INEQUALITY; HADAMARD PRODUCT; KRONECKER PRODUCT; SCHUR-CONVEX FUNCTION; MAJORIZATION;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
15
Recensione:
Indirizzi per estratti:
Citazione:
B.Y. Wang e F.Z. Zhang, "TRACE AND EIGENVALUE INEQUALITIES FOR ORDINARY AND HADAMARD-PRODUCTS OF POSITIVE SEMIDEFINITE HERMITIAN MATRICES", SIAM journal on matrix analysis and applications, 16(4), 1995, pp. 1173-1183

Abstract

Let A and B be n x n positive semidefinite Hermitian matrices, let alpha and beta be real numbers, let o denote the Hadamard product of matrices, and let A(k) denote any k x k principal submatrix of A. The following trace and eie;envalue inequalities are shown: tr(A o B)(alpha) less than or equal to tr(A(alpha) o B-alpha), alpha less than or equalto 0 or alpha greater than or equal to 1, tr(A o B)(alpha) greater than or equal to tr(A(alpha) o B-alpha), 0 less than or equal to alpha less than or equal to 1, lambda(1/alpha) (A(alpha) o B-alpha) less thanor equal to lambda(1/beta) (A(beta) o B-beta), alpha less than or equal to beta, alpha beta not equal 0, lambda(1/alpha) [(A(alpha))(k)] less than or equal to lambda(1/beta) [(A(beta))(k)], alpha less than or equal to beta, alpha beta not equal 0. The equalities corresponding tothe inequalities above and the known inequalities tr(AB)(alpha) less than or equal to tr(A(alpha) o B-alpha), /alpha/ greater than or equalto 1, and tr(AB)(alpha) greater than or equal to tr(A(alpha)B(alpha)), /alpha/ less than or equal to 1 are thoroughly discussed. Some applications are given.

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Documento generato il 28/09/20 alle ore 05:36:40