两个矩阵同时化为Hermite标准型的一个充分必要条件

A Necessary and Sufficient Condition for Two Matrices Synchronously into Hermite Canonical Forms

利用单纯的矩阵方法得到,两个同型矩阵A,B能够同时化为Hermite标准型的一个充分必要条件是rank(A+B)=ran kA+ran kB.在此基础上,若同型矩阵序列A1,A 2,...,At满足rank(A1+…+At)=rank A1+…+rank At,则对任意两个矩阵Ai,Aj(i≠j)均可以同时化为Hermite标准型.

By using methods of matrix, two matrices A,B with the same dimensions were transformed synchronously into Hermite canonical forms if and only if rank（A ＋ B） = rankA ＋ rankB. On this basis, for series of matrix with the same dimensions A1,A2….,Ai, all Ai and Aj（i≠j）） could be transformed synchronously into Hermite canonical forms if rank（A1 ＋… ＋ Ai） = rankA1 ＋… ＋ rankA.