An extension problem for H-unitary matrices with applications to Hermitian Toeplitz matrices

Roland Freund; Thomas Huckle

doi:10.1016/0024-3795(88)90189-9

An extension problem for H-unitary matrices with applications to Hermitian Toeplitz matrices

Roland Freund
, Thomas Huckle

University of Würzburg

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

1 Scopus citations

Abstract

Given a Hermitian matrix H, a matrix U is said to be H-unitary if U^HHU = H. We consider the following extension problem: If U₀ is a rectangular matrix such that U^H₀HU₀ = A, where A is a leading principal submatrix of H, can U₀ be extended to an H-unitary matrix? After presenting necessary conditions for a more general situation, we state a necessary and sufficient criterion for this problem and give a description of all its solutions. Finally, these results are used to derive some properties of factorizations of Hermitian Toeplitz matrices.

Original language	English
Pages (from-to)	213-230
Number of pages	18
Journal	Linear Algebra and Its Applications
Volume	108
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(88)90189-9
State	Published - Sep 1988
Externally published	Yes

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abstract = "Given a Hermitian matrix H, a matrix U is said to be H-unitary if UHHU = H. We consider the following extension problem: If U0 is a rectangular matrix such that UH0HU0 = A, where A is a leading principal submatrix of H, can U0 be extended to an H-unitary matrix? After presenting necessary conditions for a more general situation, we state a necessary and sufficient criterion for this problem and give a description of all its solutions. Finally, these results are used to derive some properties of factorizations of Hermitian Toeplitz matrices.",

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AB - Given a Hermitian matrix H, a matrix U is said to be H-unitary if UHHU = H. We consider the following extension problem: If U0 is a rectangular matrix such that UH0HU0 = A, where A is a leading principal submatrix of H, can U0 be extended to an H-unitary matrix? After presenting necessary conditions for a more general situation, we state a necessary and sufficient criterion for this problem and give a description of all its solutions. Finally, these results are used to derive some properties of factorizations of Hermitian Toeplitz matrices.

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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ER -

An extension problem for H-unitary matrices with applications to Hermitian Toeplitz matrices

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