实循环矩阵与实对角矩阵相似问题

A Problem of Similarity between Real Cyclic Matrix and Real Diagonal Matrix

本文中我们证明了与实对角矩阵相似的每一个实循环矩阵都是对称的．并给出了一个正交变换，使得任意的ｎ×ｎ实循环对称矩阵通过该变换与实对角矩阵相似．

In this paper, We prove that every real cyclic matrix, which is similar to a real diagonal matrix. must be symmetric. Furthermore,we construct an orthogonal transformation such that any n×n real cyclicsymmetric matrix is similar to a real diagonal matrix by the transformation.