两类对称箭形矩阵的逆问题

Two Inverse Problems of Symmetric Arrow-Head Matrice

研究了2类矩阵逆特征值问题.给定4个同维数的列向量,求对称箭形矩阵逆问题有解的条件.得到了该问题有解的充分必要条件,给出了求解的方法.给定2个同维数的向量,求对称箭形矩阵逆问题的最小二乘解.证明该问题一定有解,并给出了解的表达式以及求解的算法.

Two matrix inverse problems were considered, One was the symmetric arrow-head matrix inverse problem for four given column vectors of the same length. We have obtained the necessary and sufficient conditions for its consistency, and have given the method to compute the solutions. Another was the least-square problems for two given column vectors of the same length. We have proved that the problem always has a solution, and provide an algorithm to compute the least-square solutions .