CAJ | 학술논문

两个数域上的数字矩阵的相似问题可以转化为其相应的特征矩阵等价的命题来解决。很多教科书对这一问题的证明过于简单，没有真正的区分数字矩阵和多项式矩阵之间的不同。数字矩阵与多项式矩阵的区别就在于数字矩阵经过加法、减法、乘法、除法后还是数字矩阵，但多项式矩阵不能无条件的进行除法运算后还是多项式矩阵。所以，我们在证明多项式矩阵的有些问题时，不能直接套用数字矩阵的一些命题和定理。本文对“数字矩阵相似”等价于“特征矩阵等价”这一问题进行了详细论述。
량개수역상적수자구진적상사문제가이전화위기상응적특정구진등개적명제래해결。흔다교과서대저일문제적증명과우간단，몰유진정적구분수자구진화다항식구진지간적불동。수자구진여다항식구진적구별취재우수자구진경과가법、감법、승법、제법후환시수자구진，단다항식구진불능무조건적진행제법운산후환시다항식구진。소이，아문재증명다항식구진적유사문제시，불능직접투용수자구진적일사명제화정리。본문대“수자구진상사”등개우“특정구진등개”저일문제진행료상세논술。
The problem about digital matrix’s similarity can be solved with the equivalence of the corresponding characteristic matrix.In many textbooks the proof of this problem is too simple; they haven’ t made a distinction between the digital matrix and the polynomial matrix.The difference between digital matrix and polynomial matrix is that the digital matrix is still digital matrix through the operation of addition, subtraction, multiplication, and division, but the polynomial matrix is not.So, when we prove some problems about polynomial matrix, it can not be used directly with the digital matrix’ s definitions and theorems.This article has discussed in detail this problem that "digital matrix’ s similarity” is equivalent to “the equivalence of characteristic matrix”.