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第十五讲 投影矩阵与Moore-Penrose逆一投影算子与投影矩阵设LM为的子空间并构成直和.即唯一的使x=yz称y为x沿着M到L的投影1. 定义:将任意变为其沿着M到L的投影的变换称为沿着M到L的投影算子记为即投影算子是线性变换其矩阵称为投影矩阵仍记为2. 充要条件 引理:设n阶方阵E为幂等矩阵则证明: 即则定理:n阶方阵P成为投影矩阵的充要条件是P为幂等矩阵证明:充分性若 确为
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