On a Question of P. R. Haimos

Xingzhi Zhan

doi:10.1080/03081089508818398

On a Question of P. R. Haimos

Xingzhi Zhan

Fudan University

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

Abstract

Given a matrix A, determine δ(A) = inf{∥A − P∥ : 0 ≤ P ≤ 1} and find a P for which the infimum is attained. We solve this problem for arbitrary A in the Frobenius norm and for normal matrices in the spectral norm. A necessary and sufficient condition is presented for a normal matrix to have a unique approximant in the spectral norm.

Original language	English
Pages (from-to)	255-258
Number of pages	4
Journal	Linear and Multilinear Algebra
Volume	39
Issue number	3
DOIs	https://doi.org/10.1080/03081089508818398
State	Published - 1 Aug 1995
Externally published	Yes

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AB - Given a matrix A, determine δ(A) = inf{∥A − P∥ : 0 ≤ P ≤ 1} and find a P for which the infimum is attained. We solve this problem for arbitrary A in the Frobenius norm and for normal matrices in the spectral norm. A necessary and sufficient condition is presented for a normal matrix to have a unique approximant in the spectral norm.

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On a Question of P. R. Haimos

Abstract

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