LU factorization for rectangular matrix seems incomplete

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Soo Chang Choe
Soo Chang Choe 2018-11-18
评论： Soo Chang Choe 2018-11-19
The following example shows 3x4 maxtrix lu factorization in MATLAB seems incomplete.
MATLAB's answer for u is [1 3 3 2; 0 0 3 3; 0 0 6 6].
The answer in the text book (Gilbert Strang) is [1 3 3 2; 0 0 3 3; 0 0 0 0].
Is thera a way to get the same answer as the one from the text book through MATLAB?
----------------------------------------------------------------------------------------------------------
a =
[ 1, 3, 3, 2]
[ 2, 6, 9, 7]
[ -1, -3, 3, 4]
>> [l,u,p]=lu(a)
l =
[ 1, 0, 0]
[ 2, 1, 0]
[ -1, 0, 1]
u =
[ 1, 3, 3, 2]
[ 0, 0, 3, 3]
[ 0, 0, 6, 6]
p =
1 0 0
0 1 0
0 0 1
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Bruno Luong
Bruno Luong 2018-11-19
编辑：Bruno Luong 2018-11-19
"I don't understand why it stopped pivoting at the second row."
It does NOT stop, at the second step it pivots at the diagonal elements which is 0 for both row 2 and 3 (draw) so it picks row 2. Elements above/on the right the diagonal of u are not supposed to play any role.
In your book it selects row 3, but it is just a choise, without any additional usefulness for what it design for: solving linear system.
Both are equally valid.
Soo Chang Choe
Soo Chang Choe 2018-11-19
Hello Bruno,
I wanted to use MATLAB to check my answer when studying the text book.
It seems that I have to build my own funciton to get the answer that the book expects for now.
As you said, I am convinced that MATLAB is generating valid answers for LU decomposition.
Many thanks for your reply and answer.

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