【摘要】 通过对自伴矩阵的深入分析和讨论,给出了自伴矩阵的特征值及特征向量的性质;证明了自伴矩阵一定可以酉相似于对角阵;得到了Hermite二次型可通过可逆线性变换化为标准形的一般方法以及Hermite二次型正定的几个充要条件。更多还原

【Abstract】 Based on a through analysis and discussion of independent companion matrix,this paper presents the properties of the characteristic value and the characteristic vector of independent companion matrix.It provides the proof that independent companion matrix is unitary congruent with a opposite angles matrix.It presents the general method to transform the Hermite quadratic form into the standard form based on the contrary line transformation,and provides several necessary and sufficient conditions of the positive Hermite quadratic form.更多还原