一类矩阵多项式秩的恒等式与应用  

Identities and application of the rank of a class of matrices polynomials

作　　者：胡付高[1] 曾玉娥[1] 

机构地区：[1]孝感学院数学系,湖北孝感432000

出　　处：《山东大学学报（理学版）》2008年第8期51-54,共4页Journal of Shandong University(Natural Science)

摘　　要：给出了矩阵秩的Frobenius不等式取等号的一个充分条件,在此基础上获得了一类矩阵多项式秩的恒等式。利用这些秩的恒等式统一推广了近期一些文献中的相关结论,最后利用所得结论发现并修正了一些文献中的错误。A sufficient condition about the Frobenius inequality of the rank of a matrix, when it is equivalent, was given. Based on this, some identities of the rank of a class of matrix polynomials were obtained. Using these identities, some relevant conclusions in the recent literature were generalized and some errors were also found and corrected.

关 键 词：矩阵多项式 互素多项式 矩阵的秩 

分 类 号：O151.21[理学—数学]