矩阵的那些性质与应用-迹Tr(A)、转置

矩阵乘法运算满足如下基本性质: 1.\(({\bf{AB}}){\bf{C}} = {\bf{A}}({\bf{BC}})\) 2.\({\bf{A}}({\bf{B}} + {\bf{C}}) = {\bf{AB}} + {\bf{AC}}\) 但不满足交换律\({\bf{AB}} \ne {\bf{BA}}\) 转置满足的性质: 1.\({({\bf{A}} + {\bf{B}})^T} = ({{\bf{A}}^T} + {{\bf{B}}^T})\) 2.\({({\bf{AB}})^T} = {{\bf{B}}^T}{{\bf{A}}^T}\) 定义:若A是方阵,称其对角线元素之和为A的迹,记作Tr(A),即: \[Tr({\bf{A}}) = \sum\limits_{i = 1}^n {{a_{ii}}} \] 性质1:设A为n阶方阵,则有 \[Tr({\bf{A}}) = Tr({{\bf{A}}^T})\] 性质2:若A、B都是n阶方阵,则有 \[Tr({\bf{AB}}) = … 继续阅读