一类伪Jacobi矩阵的广义逆特征问题

Generalized inverse eigen-problem of a class of pseudo-Jacobi matrices

研究了由一个Jacobi矩阵,两个不同的实数以及两个不同的列向量确定一类非奇异伪Jacobi矩阵,使得给定Jacobi矩阵为所确定的伪Jacobi矩阵的顺序主子阵,给定两个不同的实数为此非奇异伪Jacobi矩阵的特征值,且给定两个列向量为这两个实数所对应的特征向量中的一部分。得到了这类矩阵广义逆特征问题有唯一解的充要条件,并且利用此充要条件找到了一个具体的矩阵,验证了所给条件的正确性。

A class of non-singular pseudo-Jacobi matrices are determined by a Jacobi matrix,two different real numbers and two different column vectors such that the Jacobi matrix is its leading principal submatrix,and these two different real numbers are the eigenvalues of the non-singular pseudo-Jacobi matrix,and these two column vectors are part of the eigenvectors corresponding to these two real numbers.The necessary and sufficient conditions for the unique solution of the generalized inverse eigenvalue problem of this kind of matrix are obtained.An example is given to verify the correctness of the given condition.