Norm-preserving dilation theorems for a block positive semidefinite (definite) matrix

DOI10.1080/03081087.2021.2008854zbMath1516.15003OpenAlexW4200156459WikidataQ113851278 ScholiaQ113851278MaRDI QIDQ6039179

Xifu Liu

Publication date: 3 May 2023

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2021.2008854

zbMATH Keywords

positive definite matrixblock matrixpositive semidefinite matrixspectral normnorm-preserving dilation

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Conditioning of matrices (15A12)

Cites Work

• Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm
• Minimum rank Hermitian solution to the matrix approximation problem in the spectral norm and its application
• Minimum rank (skew) Hermitian solutions to the matrix approximation problem in the spectral norm
• Norm-Preserving Dilations and Their Applications to Optimal Error Bounds
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Further Study and Generalization of Kahan’s Matrix Extension Theorem
• Minimum Rank Solutions to the Matrix Approximation Problems in the Spectral Norm

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