Singular value decomposition of multi-companion matrices

Georgi N. Boshnakov

doi:10.1016/j.laa.2007.02.010

Singular value decomposition of multi-companion matrices

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

Abstract

We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V, from the columns of U. We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic. © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	393-404
Number of pages	11
Journal	Linear Algebra and its Applications
Volume	424
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2007.02.010
Publication status	Published - 15 Jul 2007

Keywords

Companion matrix
Multi-companion matrix
Polar decomposition
SVD

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10.1016/j.laa.2007.02.010

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title = "Singular value decomposition of multi-companion matrices",

abstract = "We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V, from the columns of U. We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

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T1 - Singular value decomposition of multi-companion matrices

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PY - 2007/7/15

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N2 - We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V, from the columns of U. We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic. © 2007 Elsevier Inc. All rights reserved.

AB - We obtain the singular value decomposition of multi-companion matrices. We completely characterise the columns of the matrix U and give a simple formula for obtaining the columns of the other unitary matrix, V, from the columns of U. We also obtain necessary and sufficient conditions for the related matrix polynomial to be hyperbolic. © 2007 Elsevier Inc. All rights reserved.

KW - Companion matrix

KW - Multi-companion matrix

KW - Polar decomposition

KW - SVD

U2 - 10.1016/j.laa.2007.02.010

DO - 10.1016/j.laa.2007.02.010

M3 - Article

SN - 0024-3795

VL - 424

SP - 393

EP - 404

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 2-3

ER -

Singular value decomposition of multi-companion matrices

Abstract

Keywords

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