| 摘要: |
| 给定〖WTHX〗X,B∈R〖WTBZ〗n×m和正整数s，在集合〖WTHX〗W〖WTBZ〗-1〖WTHX〗ASR〖WTBZ〗n×n中寻找矩阵方程〖WTHX〗AX=B的解A〖WTBZ〗，使得r(〖WTHX〗A〖WTBZ〗)=s；当解集S1={〖WTHX〗A〖WTBZ〗∈〖WTHX〗W〖WTBZ〗-1〖WTHX〗ASR〖WTBZ〗n×n〖JB(|〗〖WTHX〗AX=B〖WTBZ〗〖JB)〗}非空时，记m〖DD(-*2〗〖KG*4〗〖HT〗~〖DD)〗=min〖DD(X〗〖WTHX〗A〖WTBZ〗∈S1〖DD)〗 r(〖WTHX〗A〖WTBZ〗),M〖DD(-*2〗〖HT〗~〖DD)〗=max〖DD(X〗A∈S1〖DD)〗 r(〖WTHX〗A〖WTBX〗)，在S1中确定最大、最小秩解。 |
| 关键词: 准反对称矩阵 矩阵方程 最大秩 最小秩 |
| DOI： |
| 分类号: |
| 基金项目: |
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| The W para anti symmetric Minimal Rank Solution of the Matrix Equation AX=B |
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DU Yu xia，LIANG Wu，FEI Shi long
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| Abstract: |
| Given X,B∈Rn×m，and a positive integer s，search A∈W-1ASRn×n for A of AX=B,to make r(A)=s.When the solution set S1={A∈W-1ASRn×n〖JB(|〗AX=B〖JB)〗} is nonempty，m〖DD(-*2〗〖KG*4〗〖HT〗~〖DD)〗=min〖DD(X〗A∈S1〖DD)〗 r(A),M〖DD(-*2〗〖HT〗~〖DD)〗=max〖DD(X〗A∈S1〖DD)〗 r(A)，and determine the W para anti symmetric minimal and maximal rank solutions in S1 |
| Key words: W para anti symmetric matrix matrix equation maximal rank minimal rank |
