特殊分块矩阵的Jordan标准形及应用

摘要

Jordan canonical form is an important class of canonical form in matrix analysis. This pa- per uses the method of mathematics induction to prove the Jordan canonical form of four special block matrixes and apply it to discussion the number and size of the Jordan block associated with an eigenval- ue of the Kronecker product of two matrixes.%Jordan标准形是矩阵分析中一类重要的标准形。利用数学归纳法，证明4种特殊分块矩阵的Jordan标准形，并且应用所得的结果证明两个矩阵Kronecker的特征值所对应Jordan块的个数及其阶。