MIT线性代数笔记-第四讲

Elimination=Factorization:A = LU

The factors Land U are triangular matrices. The factorization that comes from elimination is A = L U.
由消去法可知,A可以分解为LU(这是没有row exchange的情况)。
The entries of L are exactly the multipliers eij-which multiplied the pivot row j when it was subtracted from row i.
L中的项即为消去法中对应的乘子

例子:

The second line is our factorization LV = A. Instead of E:;l we write L. Move now to larger matrices with many E’s. Then L will include all their inverses.
多个矩阵的逆需要将顺序颠倒，例如:
E21E31E32A=U$E_{21}{E}_{31}{E}_{32}A=U$ becomes A=E−121E−131E−132U$A=E_{21}^{-1}{E}_{31}^{-1}{E}_{32}^{-1}U$,也就是A = LU

Better Balance