Displaying similar documents to “Finite generating system of matrix invariants.”

Conjugacy and factorization results on matrix groups

Thomas Laffey (1994)

Banach Center Publications

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In this survey paper, we present (mainly without proof) a number of results on conjugacy and factorization in general linear groups over fields and commutative rings. We also present the additive analogue in matrix rings of some of these results. The first section deals with the question of expressing elements in the commutator subgroup of the general linear group over a field as (simple) commutators. In Section 2, the same kind of problem is discussed for the general linear group over...

Infinite elementary divisor structure-preserving transformations for polynomial matrices

Nicholas Karampetakis, Stavros Vologiannidis (2003)

International Journal of Applied Mathematics and Computer Science

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The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where...