关于复Hermite阵与实对称阵的相似

On Complex Hermite Matrices Similar to Real Symmetric Matrices

某些复Hemite矩阵通过对角的酉相似就可变换到与复Hermite矩阵同形状的实对称矩阵。这样,借助于丰富的实对称阵的特征值算法,不用复的运算就可计算这些复Hermite阵特征对。这样的复Hermite矩阵包括了三对角的和箭形的矩阵。但是这样的Hermite矩阵可能不多,结果较难以推广。文中用一个简单的例子对这一点加以了说明。

There are some complex Hermitian matrices that can be transformed into real symmetric matrices of the same zero pattern by diagonal unitarily similarity.Therefore,having the aid of real symmetric matrices eigenproblem algorithms,the eigenpairs of the class of the matrices can be easily computed without need of any complex arithmetic.Such complex Hermitian matrices include tridiagonal and arrow matrices.However,there may be few of such Hermitian matrices,and the result can hardly be extended.We give a simple example to illustrate this.