可逆矩阵的高次伴随矩阵

High Degree Adjoint Matrix for Invertible Matrix

用数学归纳法推出了可逆矩阵的高次伴随矩阵的公式,并结合可逆矩阵的基本公式得出了可逆矩阵的高次伴随矩阵的行列式和逆矩阵,给出了可逆矩阵的高次伴随矩阵的特征值和特征向量的表示公式,最后讨论了若干个可逆矩阵的乘积的高次伴随矩阵.

In this paper, we introduce formulas of the high degree adjoint matrix for invertible matrix with mathematical induction, we also get determinant and inverse matrix of the high degree adjoint matrix for invertible matrix with basic formulas of invertible matrix, we also get formulas of characteristic root and characteristic vector of the high degree adjoint matrix for invertible matrix, finally we discuss the high degree adjoint matrix for the product of finite invertible matrix.