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线性回归求解时提到:
因为 N >> d+1 ,所以 的逆矩阵通常都是存在的。
为什么?
The text was updated successfully, but these errors were encountered:
从 Col 上的角度分析矩阵乘积:
因为 X 是一个 N x d+1 的矩阵,N >> d+1,所以 X 的 Col 是独立的; 的每个 Col 可以看成是 X 的每一个 Col 通过矩阵 得到的,所以 的每个 Col 也是独立的(否则与 X 的 Col 是独立的矛盾),所以逆矩阵存在。
或者用 Composition 的思路:
这个矩阵,可以看成是 和 X 两个线性系统的连接。
输入是一个 d+1 维的向量,先输入 X 这个系统,输出 N 维的向量;然后输入 这个系统,输出 d+1 维的向量。 因为 N >> d+1,从低维空间到高维空间的转化是可逆的,所以 这个系统是可逆的,所以逆矩阵存在。
呃,感觉很不严谨...甚至有可能错了....
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[FIX] Fix invertible (#3)
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Lecture 9: Linear Regression
线性回归求解时提到:
为什么?
The text was updated successfully, but these errors were encountered: