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

LU factorization for rectangular matrix seems incomplete

Bruno Luong 2018-11-18

编辑：Bruno Luong 2018-11-18

Are you runing MATLAB or something else? Your formatting seems not to be MATLAB and your result does not match mine (R2018a).

a
a =
     1     3     3     2
     2     6     9     7
    -1    -3     3     4
>>  [l,u,p]=lu(a)
l =
   1.000000000000000                   0                   0
   0.500000000000000   1.000000000000000                   0
  -0.500000000000000                   0   1.000000000000000
u =
   2.000000000000000   6.000000000000000   9.000000000000000   7.000000000000000
                   0                   0  -1.500000000000000  -1.500000000000000
                   0                   0   7.500000000000000   7.500000000000000
p =
     0     1     0
     1     0     0
     0     0     1

Soo Chang Choe 2018-11-18

run 'a = sym(a);' before lu() function. You will get the same format.

However, your numerical results also have the same problem. U's last row should be [0 0 0 0], but it is not.

Bruno Luong 2018-11-18

Why there is "problem" or "incomplete"? It's upper triangular as advertised.

For your information LU factorization is not unique.

Soo Chang Choe 2018-11-19

编辑：Soo Chang Choe 2018-11-19

Mathematically it is not a problem or incomplete. But is there a built-in matlab funciton that gives me the same answer as can be found in the text book? I don't understand why it stopped pivoting at the second row.

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 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.

LU factorization for rectangular matrix seems incomplete

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