矩阵分解在生活中有哪些应用？ 矩阵分解在生活中有哪些应用
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\u4f8b\u5982A=[1 1 1 \u03b1=(x
2 3 4 y
1 2 3] z)
\u5219A\u03b1=(x+y+z
2x+3y+4z
x+2y+3z)
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A=[1 1 [1 0 -1
2 3 * 0 1 2]
1 2]
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\u5219A\u03b1=[1 1 [1 0 -1 (x
2 3 * 0 1 2] * y
1 2] z)
=[1 1 (x-z
2 3 * y+2z)
1 2]
=(x+y+z
2x+3y+4z
x+2y+3z)
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\u4f8b\u5982A=[1 1 1 \u03b1=(x
2 3 4 y
1 2 3] z)
\u5219A\u03b1=(x+y+z
2x+3y+4z
x+2y+3z)
\u5373\u77e9\u9635\u5b9e\u8d28\u4e0a\u662f\u4e00\u79cd\u7ebf\u6027\u53d8\u6362\u7b97\u7b26.
A=[1 1 [1 0 -1
2 3 * 0 1 2]
1 2]
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\u5219A\u03b1=[1 1 [1 0 -1 (x
2 3 * 0 1 2] * y
1 2] z)
=[1 1 (x-z
2 3 * y+2z)
1 2]
=(x+y+z
2x+3y+4z
x+2y+3z)
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例如A=[1 1 1 α=(x
2 3 4 y
1 2 3] z)
则Aα=(x+y+z
2x+3y+4z
x+2y+3z)
即矩阵实质上是一种线性变换算符。
<二>A=[1 1 [1 0 -1
2 3 * 0 1 2]
1 2]
这里以及下面为了表示方便，引入符号*表示矩阵乘法，遵循矩阵乘法规则。
则Aα=[1 1 [1 0 -1 (x
2 3 * 0 1 2] * y
1 2] z)
=[1 1 (x-z
2 3 * y+2z)
1 2]
=(x+y+z
2x+3y+4z
x+2y+3z)
即矩阵分解实质上是将原来的线性变换等效为两次线性变换（或多次线性变换，如果分解后矩阵可以继续分解）
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