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ELA

A NEW DECOMPOSITION FOR SQUARE MATRICES

∗

JULIO BEN´ıTEZ†

Abstract. A new decomposition is derived for any complex square matrix. This decomposition is based on the canonical angles between the column space of this matrix and the column space of its conjugate transpose. Some applications of this factorization are given; in particular some matrix partial orderings and the relationship between the canonical angles and various classes of matrices are studied.

Key words.Decomposition of matrices, EP matrices, Canonical angles, Matrix partial ordering.

AMS subject classifications.15A23, 15A57.

∗Received by the editors November 17, 2009. Accepted for publication April 2, 2010. Handling

Editor: Roger A. Horn.

†Departamento de Matem´atica Aplicada, Instituto de Matem´atica Multidisciplinar, Universidad

Polit´ecnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain. ([email protected]).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 207-225, April 2010

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