矩阵的秩与非零特征值个数差的确定

摘要

Taking the Jordan canonical form as a basic tool,we showed the determination method of the difference between the rank of matrix’s power and the number of non-zero eigenvalues,with its result independent of the Jordan canonical form.%以矩阵的 Jordan 标准形为工具，给出了用矩阵方幂的秩表示的矩阵的秩和非零特征值个数差的确定方法，其结果不依赖于矩阵的 Jordan 标准形。