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[再寄小读者之数学篇](2014-05-18 从正定矩阵构造正定矩阵)

A<script id="MathJax-Element-1" type="math/tex">{\bf A}</script> 为 n<script id="MathJax-Element-2" type="math/tex">n</script> 阶正定矩阵, x<script id="MathJax-Element-3" type="math/tex">{\bf x}</script>, y<script id="MathJax-Element-4" type="math/tex">{\bf y}</script> 为 n<script id="MathJax-Element-5" type="math/tex">n</script> 维列向量且满足 xty>0<script id="MathJax-Element-6" type="math/tex">{\bf x}^t{\bf y}>0</script>. 证明矩阵

M=A+xxtxty?AyytAytAy
<script id="MathJax-Element-7" type="math/tex; mode=display">\bex {\bf M}={\bf A}+\cfrac{{\bf x}{\bf x}^t}{{\bf x}^t{\bf y}} -\cfrac{{\bf A}{\bf y}{\bf y}^t{\bf A}}{{\bf y}^t{\bf A}{\bf y}} \eex</script> 正定.