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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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128000021X |
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| _version_ | 1832554611619135488 |
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| author | A. Duane Porter Nick Mousouris |
| author_facet | A. Duane Porter Nick Mousouris |
| author_sort | A. Duane Porter |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0a4ff3598bff4788b2830faa4b2f7cf8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0a4ff3598bff4788b2830faa4b2f7cf82025-02-03T05:50:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013229330410.1155/S016117128000021XRanked solutions of the matric equation A1X1=A2X2A. Duane Porter0Nick Mousouris1Mathematics Department, University of Wyoming, Laramie 82070, Wyoming, USAMathematics Department, Humboldt State University, Arcata 95521, California, USALet 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.http://dx.doi.org/10.1155/S016117128000021Xfinite fieldmatric equationranked solutions. |
| spellingShingle | A. Duane Porter Nick Mousouris Ranked solutions of the matric equation A1X1=A2X2 International Journal of Mathematics and Mathematical Sciences finite field matric equation ranked solutions. |
| title | Ranked solutions of the matric equation A1X1=A2X2 |
| title_full | Ranked solutions of the matric equation A1X1=A2X2 |
| title_fullStr | Ranked solutions of the matric equation A1X1=A2X2 |
| title_full_unstemmed | Ranked solutions of the matric equation A1X1=A2X2 |
| title_short | Ranked solutions of the matric equation A1X1=A2X2 |
| title_sort | ranked solutions of the matric equation a1x1 a2x2 |
| topic | finite field matric equation ranked solutions. |
| url | http://dx.doi.org/10.1155/S016117128000021X |
| work_keys_str_mv | AT aduaneporter rankedsolutionsofthematricequationa1x1a2x2 AT nickmousouris rankedsolutionsofthematricequationa1x1a2x2 |