体上代数矩阵的素有理标准形与特征值

The Primary Rational Canonical Form and Eigenvalues of Algebraic Matrix over a Skew Field

本文应用最小中心多项式给出了体上代数矩阵的素有理标准形与初等因子组的构造，由此得到体上代数矩阵相似的充要条件以及相似于一个对角矩阵的充要条件．本文还讨论了体上矩阵的左、右特征值的构造与性质．

Let D be any skew field, by using the minimal central polynomial, this paper gives the structure of the primary rational canonical form and the elementary divisors of any algebraic matrix over D, obtains the necessary and sufficient condition that two algebraic matrices over D are similar, and the necessary and sufficient condition that a algebraic matrix over D is similar to a diagonal matrix. This paper also discusses the structure and properties of the left or right eigenvalue of a matrix over D.