Factorization of matrices into partial isometries

Authors:
Kung Hwang Kuo and Pei Yuan Wu

Journal:
Proc. Amer. Math. Soc. **105** (1989), 263-272

MSC:
Primary 15A23; Secondary 47A68

DOI:
https://doi.org/10.1090/S0002-9939-1989-0977922-1

MathSciNet review:
977922

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we characterize complex square matrices which are expressible as products of partial isometries and orthogonal projections. More precisely, we show that a matrix is the product of partial isometries if and only if is a contraction and rank nullity . It follows, as a corollary, that any singular contraction is the product of partial isometries and is the smallest such number. On the other hand, is the product of finitely many orthogonal projections if and only if is unitarily equivalent to , where is a singular strict contraction . As contrasted to the previous case, the number of factors can be arbitrarily large.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0977922-1

Keywords:
Partial isometry,
orthogonal projection,
contraction,
idempotent matrix

Article copyright:
© Copyright 1989
American Mathematical Society