# Accession Number:

## ADA043732

# Title:

## A Linear Algebra Problem Over Finite Fields.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1977-08-01

# Pagination or Media Count:

## 17.0

# Abstract:

Let K GFq denote the finite field of order q, let G denote the group of one-to-one maps permutations of K onto K, and let GLn,K denote the group of n x n invertible matrices over K. Each triple alpha1, alpha2,A elements of GxGxGLn,K determines a permutation of the vector space K super n, of n x 1 matrices over K as follows PiX alpha1 inverse A alpha2X X element of K super n, where alpha1, acts on X component-wise and A acts on x via matrix multiplication. Two triples alpha1, alpha2,A and beta1, beta2,B are called equivalent if they determine the same permutation II. This paper determines for given alpha1, alpha2, A those equivalent beta1, beta2, B.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics