等价的一个性质

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-04-01 DOI:10.6028/JRES.078B.011

M. Newman

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引用次数: 2

摘要

设R是一个主函数，如果a和B是R上相等的矩阵(参见[1])，则我们写a e B。任意两个矩阵A和B的Kronecke r积由A @ B表示，下面的结果由W. D. Wallis在他的论文[2]中所作的评论得到:定理:假设K, A, r上的裸露非奇异矩阵使得K @ AE K @ B，则AEB。实际上，没有必要假定A和Bare是非正则的，但是这样做可以简化说明。我们首先证明下面的引理:假设集合

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A property of equivalence

Let R be a prin cipal id eal rin g. W e write A E B, if A and B a re matrices over R wh ich are equivale nt (see [1] for a co mple te di scussion of thi s topic). The Kronecke r product of any two matrices A and B will be de noted by A @ B. The follow in g res ult was s ugges ted by a re mark made by W. D. Wallis in hi s s urvey paper [2]: THEOREM: Suppose that K, A, Bare nonsinguLar matrices over R such that K @ A E K @ B. Then AEB. It is not actu ally necessary to assume that A and Bare nonsin gular , bu t doin g so simpljfies the exposi ti on. We firs t prove th e followin g: LEMMA: Suppose that the sets

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Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences

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