特征值反问题的唯一性

The Uniqueness of Inverse Eigenvalue Problems

证明了由特征值及特征向量反求矩阵时,特征值在对角矩阵中的排序可以是任意的,只须将对应特征向量作相应排序,所得矩阵唯一。对于重特征值的线性无关的特征向量可任意选取,所得矩阵唯一。

For the given eigenvalues and corresponding independent eigenvectors,there exists a unique matrix no matter how the eigenvalues are sorted in the diagonal of diagonal matrix and no matter how the corresponding eigenvectors are selected.