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)
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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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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.
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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