Ranked solutions of the matric equation A1X1=A2X2

Ranked solutions of the matric equation A1X1=A2X2

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...

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Veröffentlicht in:International journal of mathematics and mathematical sciences 1980-01, Vol.3 (2), p.293-304
Hauptverfasser: A. Duane Porter, Nick Mousouris
Format: Artikel
Sprache:eng
Schlagworte:
finite field
matric equation
ranked solutions
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Zusammenfassung: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/S016117128000021X