矩阵空间M_(2)(C)中正规矩阵的表示形式及应用  

Representation and Application of Normal Matrix on Matrix Space M_(2)(C)

作　　者：任芳国[1] 禹鸥洋 REN Fangguo;YU Ouyang(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,Shaanxi,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《咸阳师范学院学报》2024年第2期5-9,共5页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(11471200)。

摘　　要：正规矩阵是一种具有良好性质的特殊重要矩阵。根据正规矩阵的定义,利用矩阵运算、特征值及矩阵范数,研究了矩阵空间M_(2)(C)中正规矩阵的表示形式及几个典型应用。讨论了矩阵空间M_(2)(C)中由正规矩阵构成的标准正交基、正交基及基,深化了Pauli矩阵的性质,这些结果充实并完善了二阶正规矩阵的理论结果。A normal matrix is a special and important matrix with good properties.According to the definition of normal matrix,the representation form and several typical applications of normal matrix in matrix space M_(2)(C)were studied using matrix operations,eigenvalues,and matrix norms,secondly,the standard orthogonal bases,orthogonal bases,and bases composed of normal matrices in matrix space M_(2)(C)are discussed,andthe properties of Pauli matrices are deepened,these results enrich and improve the theoretical results of second-order normal matrices.

关 键 词：矩阵空间 正规矩阵 酉矩阵 Pauli矩阵 

分 类 号：O151.21[理学—数学]