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The semigroup generated by a unitary orbit of a singular matrix |
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| Authors: | H Radjavi A R Sourour |
| Institution: | a Department of Pure Mathematics, University of Waterloo, Waterloo Ontario,, N2L 3G1, Canada |
| Abstract: | We investigate the structure of the multiplicative semigroup generated by the set of matrices that are unitarily equivalent to a given singular matrix A. In particular, we give necessary and sufficient conditions, in terms of the singular values of A, for such a semigroup to consist of all matrices of rank not exceeding the rank of A. |
| Keywords: | Unitary orbit Matrix semigroup Generators Factorization 2001 Mathematics Subject Classifications: Primary: 15A30 15A23 Secondary: 15A18 20M20 |
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