由k个特征对构造对称Toeplitz矩阵

Constructing a symmetric Toeplitz matrix with k prescribed eigenpairs

研究对称Toeplitz矩阵的特征值反问题.提出由给定的k个特征对构造一个实对称Toeplitz矩阵的一类特征值反问题,利用对称Toeplitz矩阵的特殊结构,矩阵的Kronecker积和拉直,将这类问题转化为一个线性代数方程组,给出由k个特征对构造对称Toeplitz矩阵有解的条件及其通解.

The inverse eigenvalue problem of symmetric Toeplitz matrix was studied. An inverse eigen- value problem was presented for constructing a real symmetric Toeplitz matrix from given k eigenpairs. By using the special structure of symmetric Toeplitz matrices, Kronecker product, and vec operator of matri- ces, this problem was transformed into a system of linear algebraic equations. Some necessary and sufficientconditions were given for the solvability of this problem. The general solutions of this problem were given, also.