正定矩阵的判定方法和新的Brauer卵形

Determination Method of Positive Definite Matrix and New Brauer Oval

利用文[郑巧娟,李耀堂。p-范数双严格对角占优矩阵与新的特征值包含区域。应用数学进展,2017,6(3):367-375。]中所给矩阵的特征值包含区域获得了实对称矩阵正定性的一种判定方法。另外,给出了一个新的正规矩阵Brauer卵形特征值包含区域,使得每个卵形至少包含矩阵的一个特征值。

The eigenvalue inclusion region in [Qiaojuan Zheng, Yaotang Li. p-Norm DSDD Matrices and New Eigenvalue Localization Region, Applied Mathematical Progress, 2017, 6(3): 367-375.] is used to obtain a method for determining the positive definite property of the real symmetric matrix. In addition, a new normal matrix Brauer oval eigenvalue inclusion region is given, so that each oval contains at least one eigenvalue of the matrix.