Semidefinite Approximations of the Matrix Logarithm

The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix functions, many of which are of importance in quantum informatio...

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Bibliographic Details
Published in:	Foundations of computational mathematics Vol. 19; no. 2; pp. 259 - 296
Main Authors:	Fawzi, Hamza, Saunderson, James, Parrilo, Pablo A.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2019 Springer Nature B.V
Subjects:	Applications of Mathematics Computer Science Concavity Convexity Economics Entropy Information theory Linear and Multilinear Algebras Math Applications in Computer Science Mathematical analysis Mathematics Mathematics and Statistics Matrix methods Matrix Theory Numerical Analysis Operators (mathematics) Optimization Quantum phenomena Solvers 52A41 Convex optimization 47A63 90C22 Matrix concavity Quantum relative entropy
ISSN:	1615-3375, 1615-3383
Online Access:	Get full text
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