Asian Research Journal of Mathematics

Irredundant and Almost Irredundant Sets in \(\mathbb{M}_2\)(\(\mathbb{C}\))

Clayton Suguio Hida *

State University of Amapa, Amapa, Brazil.

*Author to whom correspondence should be addressed.

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Abstract

We consider irredundant and almost irredundant subsets in the *-algebra \(\mathbb{M}_2\)(\(\mathbb{C}\)) of all 2 X 2 matrices with coefficients in \(\mathbb{C}\). We prove that the largest size of an irredundant subset is two, and that \(\mathbb{M}_2\)(\(\mathbb{C}\)) has an infinite almost irredundant subset.

Keywords: Matrix algebra, generators, irredundancy, involution

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