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<a href="/categories/Idea"><b>「
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</b>IDEA<b> 」</b></a>
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六月 04, 2020
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<h3 class="post-title animated fadeInDown">
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<a href="/SVD-for-homogeneous-linear-equation/" title="想法速记：SVD求齐次线性方程组 Ax=0 的解" class="posttitle">想法速记：SVD求齐次线性方程组 Ax=0 的解</a></h3>
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<b class="iconfont icon-text2"></b> <i>文章字数</i>
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2.9k
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<b class="iconfont icon-timer__s"></b> <i>阅读约需</i>
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3 mins.
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<blockquote>
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<p>原创发表于 <a href="https://blog.davidz.cn">DavidZ Blog</a>，遵循 <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode" target="_blank" rel="noopener">CC 4.0 BY-NC-SA</a> 版权协议，转载请附上原文出处链接及本声明。</p>
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</blockquote>
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<p>众所周知，SVD(奇异值分解)可以用于最小二乘法求齐次线性方程组$A\vec{x}=\vec{0}$的解。我看了很多资料，大多使用数学公式推导，得出结论。但是，曾经线性代数差点挂科的我，总觉得有些蹊跷。想了两天，终于有了一些感性的认知（不一定是对的😂），赶紧记录下来。</p>
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<p>按照我的理解，一个矩阵的实际意义是对应一个线性变换，这个变换可以理解为瞬间运动。例如，一个旋转矩阵，</p>
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<p>$$<br>
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A=\begin{bmatrix}<br>
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cos\theta & sin\theta \\\<br>
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-...</p>
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