若当矩阵幂的若当标准形

The Jordan Standard Forms of Jordan Matrices

矩阵的若当标准形在高等代数的教学中是难点之一,讨论若当矩阵幂的若当标准形既能促进教学、也有一定的理论意义,设J是若当矩阵,给出了Jk的全部初等因子及其若当标准形。

The Jordan standard form of a matrix is a difficult case in the teaching of advanced algebra. Discussing Jordan standard forms of powers of Jordan matrices is not only promoting teaching, but also is theoretically meaningful. Let J be a Jordan matrix. We give all the elementary divisors of J and its Jordan standard form in this paper.