CAJ | 학술논문

众所周知,相似矩阵的迹相等对于非交换代数和环上的矩阵不一定成立.有趣的问题是给定一个条件使得相似矩阵的迹相等对于非交换代数或非交换环上的矩阵成立.本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等.
음소주지,상사구진적적상등대우비교환대수화배상적구진불일정성립.유취적문제시급정일개조건사득상사구진적적상등대우비교환대수혹비교환배상적구진성립.본문대우특정불시2적임의역F상정의적엄의사원수대수상적량개구진A화B,급출여과A화B상사병차타문적주대각선상적원소재F중,나요타문적적상등.
The well-known trace equality of similar matrices does not necessarily hold for matrices over non-commutative algebras and rings. An interesting question is to give conditions such that trace equality of similar matrices holds for matrices over a non-commutative algebra or ring. In this note, we show that for any two matrices A and B over a generalized quaternion algebra defined on an arbitrary field F of characteristic not equal to two, if A and B are similar and the main diagonal elements of A and B are in F, then their traces are equal.