Introduction to matrix analysis and applications

zbMath1321.15004MaRDI QIDQ5892201

Fumio Hiai, Dénes Petz

Publication date: 6 October 2015

Published in: Texts and Readings in Mathematics (Search for Journal in Brave)

zbMATH Keywords

quantum theoryeigenvaluevon Neumann algebraHermitian matricesconvexitytextbooktracequantum information theorydeterminantKronecker productsubalgebraspositive matricestensor productmajorizationfunctional calculusSchur factorizationPick functionmatrix functionsmatrix analysissingular valueunitarily invariant normmatrix exponentialpartial orderingquantum Fisher informationCramer-Rao inequalitymatrix meansmatrix monotone functions\(UL\)-factorizationBoltzmann entropycanonical Jordan formcompletely positive mappingKadison's inequalitymatrix norm inequalities

Mathematics Subject Classification ID

Factorization of matrices (15A23) Determinants, permanents, traces, other special matrix functions (15A15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Algebraic systems of matrices (15A30) Multilinear algebra, tensor calculus (15A69) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra (15-01) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (13)

Matrix inequalities and majorizations around Hermite–Hadamard’s inequality ⋮ Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces ⋮ Connections between centrality and local monotonicity of certain functions on \(C^\ast\)-algebras ⋮ More on operator monotone and operator convex functions of several variables ⋮ Some families of operator norm inequalities ⋮ Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state ⋮ Matrix perspectives and matrix convexity ⋮ Some properties of weighted operator means and characterizations of interpolational means ⋮ Characterization of operator convex functions by certain operator inequalities ⋮ Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means ⋮ Matrix rearrangement inequalities revisited ⋮ Matrix Hölder-McCarthy inequality via matrix geometric means ⋮ On the joint convexity of the Bregman divergence of matrices

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