Wrong answers given by MATLAB LU Factorization

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Zhuo
Zhuo 2014-1-15
评论： José-Luis 2014-1-15
LU factorization or decomposition method is supposed to decompose a square matrix to a lower matrix and a upper matrix. However, I tried to test some 2 by 2 matrix, the MATLAB LU method sometimes give me 2 upper matrix. Such an original matrix as:
A=[4 , 3 ; 6 , 3]
The answer given by MATLAB:
[L,U]=lu(A)
L=[0.667,1 ; 1, 0]
U=[6, 3 ; 0, 1]
The correct answer should be
L=[1 , 0 ; 1.5, 1]
U=[4 , 3 ; 0, -1.5]
I don't understand why MATLAB gives me such answer
Please, someone help me!

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回答（2 个）

Sean de Wolski
Sean de Wolski 2014-1-15
The behavior you are seeing is described in Example 1 of the lu documentation:
http://www.mathworks.com/help/releases/R2013b/matlab/ref/lu.html
  1 个评论
Zhuo
Zhuo 2014-1-15
Hello, Thank you very much for your help.
I think the only way to let MATLAB to give me the correct format of lower matrix is to use: [L,U,P]=lu(A) But I have to pre-multiply the inverse of P in order to convert back to A Do you know there is a way to let MATLAB to give me an upper and a lower matrix straight away without involving intermediate matrix, such as P ?

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José-Luis
José-Luis 2014-1-15
Both answers are valid.
A = [2/3,1 ; 1, 0] *[6, 3 ; 0, 1]
B = [1 , 0 ; 1.5, 1] * [4 , 3 ; 0, -1.5]
A == B
  2 个评论
Zhuo
Zhuo 2014-1-15
Thank you very much! I know both answers are valid. However, it is very necessary to write one of the matrix in lower matrix format which is easier for my program to take further calculations.

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