关于矩阵Frobenius秩不等式的等式条件  

The Conditions for the Equality of the Frobenius Inequality on the Rank of Matrices

作　　者：龚和林[1] 舒情[1] 谭海女[1] 

机构地区：[1]上饶师范学院,上饶江西334001

出　　处：《上饶师范学院学报》2012年第3期30-34,共5页Journal of Shangrao Normal University

基　　金：江西省教育厅科技项目青年基金(GJJ10256);上饶师范学院课题(201102)

摘　　要：讨论了Frobenius秩不等式的等式问题,给出Frobenius不等式一种新证法,并得到Frobenius不等式等号成立的两个充分必要条件.进一步刻画了任一方阵的两个多项式之积为零矩阵的秩特征.In this paper, the equality problem of the Frobenius inequality of the rank of matrices was researched. A new proof for the Frobenius inequality was introduced. By this result, two necessary and sutilcient conditions for the equality of the Frobenius inequal- ity were obtained. Furthermore, this paper charactefized the properties of rank of the product of two matrix polynomials if the product is equal to null matrix.

关 键 词：秩 矩阵多项式 k次幂等矩阵 

分 类 号：O151.21[理学—数学]