Bounds for the singular values of a matrix with nonnegative eigenvalues

Izchak Lewkowicz

doi:10.1016/0024-3795(89)90586-7

Bounds for the singular values of a matrix with nonnegative eigenvalues

Izchak Lewkowicz

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

3 Scopus citations

Abstract

An upper bound and a lower bound for each singular value of a matrix with nonnegative eigenvalues are derived. These bounds are based upon the matrix spectral decomposition. It is shown that this estimate for each singular value is tighter than a well known one, based upon the condition number of the eigenvector matrix. Note, however, that the known estimate is also applicable to matrices with complex eigenvalues. A property of projection matrices, used in the proof, is discussed as well.

Original language	English
Pages (from-to)	29-37
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	112
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(89)90586-7
State	Published - 1 Jan 1989
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(89)90586-7

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abstract = "An upper bound and a lower bound for each singular value of a matrix with nonnegative eigenvalues are derived. These bounds are based upon the matrix spectral decomposition. It is shown that this estimate for each singular value is tighter than a well known one, based upon the condition number of the eigenvector matrix. Note, however, that the known estimate is also applicable to matrices with complex eigenvalues. A property of projection matrices, used in the proof, is discussed as well.",

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N2 - An upper bound and a lower bound for each singular value of a matrix with nonnegative eigenvalues are derived. These bounds are based upon the matrix spectral decomposition. It is shown that this estimate for each singular value is tighter than a well known one, based upon the condition number of the eigenvector matrix. Note, however, that the known estimate is also applicable to matrices with complex eigenvalues. A property of projection matrices, used in the proof, is discussed as well.

AB - An upper bound and a lower bound for each singular value of a matrix with nonnegative eigenvalues are derived. These bounds are based upon the matrix spectral decomposition. It is shown that this estimate for each singular value is tighter than a well known one, based upon the condition number of the eigenvector matrix. Note, however, that the known estimate is also applicable to matrices with complex eigenvalues. A property of projection matrices, used in the proof, is discussed as well.

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Bounds for the singular values of a matrix with nonnegative eigenvalues

Abstract

ASJC Scopus subject areas

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