International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 293-304
doi:10.1155/S016117128000021X

Ranked solutions of the matric equation A1X1=A2X2

A. Duane Porter1 and Nick Mousouris2

1Mathematics Department, University of Wyoming, Laramie 82070, Wyoming, USA
2Mathematics Department, Humboldt State University, Arcata 95521, California, USA

Received 8 December 1977; Revised 20 February 1979

Copyright © 1980 A. Duane Porter and Nick Mousouris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let GF(pz) denote the finite field of pz elements. Let A1 be s×m of rank r1 and A2 be s×n of rank r2 with elements from GF(pz). In this paper, formulas are given for finding the number of X1,X2 over GF(pz) which satisfy the matric equation A1X1=A2X2, where X1 is m×t of rank k1, and X2 is n×t of rank k2. These results are then used to find the number of solutions X1,…,Xn, Y1,…,Ym, m,n>1, of the matric equation A1X1…Xn=A2Y1…Ym.