Ranked solutions of the matric equation A1X1=A2X2 - A. Duane Porter; Nick Mousouris (International Journal of Mathematics and Mathematical Sciences)
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.