矩阵对角化中可逆矩阵的研究

通过对矩阵的对角化研究,找出了在对角化过程中所取的可逆阵之间的内在联系,并分别从矩阵以及线性变换两个角度给出了可逆阵之间的关系。如果n阶方阵A可对角化,则存在可逆阵P,使P-1AP为对角阵。若取可逆阵Q,Q-1AQ也为对角阵,那么适当调整Q的列向量的次序后,调整后的P,Q的列向量之间存在线性关系,且列向量之间的线性变换的矩阵为准对角矩阵,该准对角矩阵的每个块矩阵的阶数等于A的某个特征值的重数,并举例说明了这一结论。

Researches on Invertible Matrix in Diagonalizable Matrix

We find relations among invertible matrixs in diagonalization by studying of diagonalizable matrix.And we give relations of invertible matrixs from the view of matrix and linear transformation.An×n is diagonalizable if and only if there exists a invertible matrix P,such that the matrix P-1AP is a diagonal matrix.If Q is invertible,and Q-1AQ is a diagonal matrix,then there exists linear relations between column vectors of P,Q after we adjust the order of them.And the matrix of linear transition is a block diagonal matrix,and the order of each block matrix equals multiplicity of some eigenvalue.We also give an example to prove it.