The ϕ J polar decomposition of matrices with rank 2

It is known that if a matrix has a ϕ J polar decomposition, then it is of even rank. We provide necessary and sufficient conditions for a 2 n -by- 2 n matrix of rank 2 to have a ϕ J polar decomposition.

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Bibliographic Details
Published in:Linear algebra and its applications 2009, Vol.430 (2), p.756-761
Main Authors: Dato-on, Jolle E., Merino, Dennis I., Paras, Agnes T.
Format: Article
Language:English
Subjects:
[formula omitted] polar decomposition
Algebra
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Symplectic equivalence
Symplectic matrices
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Description
Summary:It is known that if a matrix has a ϕ J polar decomposition, then it is of even rank. We provide necessary and sufficient conditions for a 2 n -by- 2 n matrix of rank 2 to have a ϕ J polar decomposition.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2008.09.007