摘要
幂零矩阵及其性质在矩阵理论中有着重要应用。重点讨论了n阶方阵与幂零矩阵之间的关系问题,证明了任意n阶方阵可以分解为1个幂零矩阵与1个可对角化矩阵之和,并将该结论推广到了矩阵多项式上。最后,应用上述矩阵分解定理的证明思想,进一步给出了n阶方阵的对称矩阵分解形式。
Nilpotent matrix has important application in matrix theory. The relationship between square matrix of degree n and nilpotent matrix was explored, which testifies that square matrix of degree n can be decomposed into the sum of nilpotent matrix and diagonalization matrix. This decomposition can be applied in any matrix polynomial. Finally the above testifying method provides decomposed form for symmetric ma- trix of square matrix of degree n.
出处
《常州工学院学报》
2016年第3期48-51,共4页
Journal of Changzhou Institute of Technology
基金
湖北省教育厅科研计划资助项目(Q20156002)
汉江师范学院科研重点项目(2014A02)
关键词
幂零矩阵
对角分解
若当分解
nilpotent matrix
diagonal factorization
Jordan decomposition
