Linear spanning sets for matrix spaces

Abstract

Necessary and sufficient conditions are given on matrices $A$, $B$ and $S$, having entries in some field $\mathbb{F}$ and suitable dimensions, such that the linear span of the terms $A^{i}S{B}^j$ over $\mathbb{F}$ is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of $\mathbb{F}[A]S\mathbb{F}[B]$ when $\mathbb{F}$ is a finite field.

15 pages

References in corpus (1)

• Cryptanalysis of a non-commutative key exchange protocol

Cited by in corpus (1)

• Cryptanalysis of a non-commutative key exchange protocol