Dual operator norms and the spectra of matrices

Christoph Zenger

doi:10.1016/0024-3795(84)90225-8

Dual operator norms and the spectra of matrices

Christoph Zenger

TUM Emeriti of Excellence

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let ∥·∥ be an operator norm and ∥·∥^D its dual. Then it is shown that ∥A∥^D≥ ∑|λ_i(A)|, where λ_i(A) are the eigenvalues of A, holds for all matrices A if and only if ∥·∥ is the operator norm subordinate to a Euclidian vector norm.

Original language	English
Pages (from-to)	453-460
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	58
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(84)90225-8
State	Published - Apr 1984

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AB - Let ∥·∥ be an operator norm and ∥·∥D its dual. Then it is shown that ∥A∥D≥ ∑|λi(A)|, where λi(A) are the eigenvalues of A, holds for all matrices A if and only if ∥·∥ is the operator norm subordinate to a Euclidian vector norm.

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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ER -

Dual operator norms and the spectra of matrices

Abstract

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