| 摘要: |
| 给出整数矩阵方程Am=dI+λJ的通解,即:当d≠0时,必有(d+λn)1/m-d1/m为n的整数倍且A=d1/mI+1/n[(d+λn)1/m-d1/m]J,当d=0时,其通解为A=1/n(λn)1/meeT+1/t∑1≤j≤l;kj≥2 ∑mj=1kj-1 ζj,mj+1ηj,mjT. |
| 关键词: 矩阵方程 整数 通解 |
| DOI： |
| 投稿时间：2006-09-13 |
| 基金项目: |
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| General Solution to the Integer Matrix Equation Am=dI+λJ |
|
WU Shu-hong
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| (Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan, Hubei, 430070, China) |
| Abstract: |
| In this paper,we give general solution of integer matrix equation Am=dI+λJ,i.e.,in the case of d≠0,(d+λn)1/m-d1/m there must be integer multiple of n and A=d1/mI+1/n[(d+λn)1/m-d1/m]J;in the case of d=0,A=1/n(λn)1/meeT+1/t∑1 ≤ j ≤ l;kj ≥ 2 ∑mj=1kj-1 ζj,mj+1ηj,mjT. |
| Key words: matrix equation integer general solution |
