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On Nilpotent Subsemigroups in some Matrix Semigroups

Ganyushkin, Olexandr, Mazorchuk, Volodymyr (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 20M20, 20M10.We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with non-negative coefficients and the semigroup Dn of all doubly stochastic real matrices.

On numerical range of sp(2n, C)

Wen Yan, Jicheng Tao, Zhao Lu (2016)

Special Matrices

In this paper we studied the classical numerical range of matrices in sp(2n, C). We obtained some result on the relationship between the numerical range of a matrix in and that [...] of its diagonal block, the singular values of its off-diagonal block A2.

On orderings induced by the Loewner partial ordering

Jan Hauke, Augustyn Markiewicz (1994)

Applicationes Mathematicae

The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.

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