Solving a matrix in MATLAB?

Question

How does one solve the (non-trivial) solution Ax = 0 for x in MATLAB?

A = matrix
x = matrix trying to solve for

I've tried solve('A * x = 0', 'x') but I only get 0 for an answer.

true, but this is a limited, special-case answer to a more general problem. — Peter, Oct 04 '09 at 01:24
@Peter I think what manji is trying to say is that getting 0 is possibly the only valid result to OP particular case — BillBokeey, May 04 '16 at 15:55

Jacob · Accepted Answer · 2009-10-05T15:05:40.847

Please note that null(A) does the same thing (for a rank-deficient matrix) as the following, but this is using the svd(A) function in MATLAB (which as I've mentioned in my comments is what null(A) does).

[U S V] = svd(A);
x = V(:,end)

For more about this, here's an link related to this (can't post it to here due to the formulae).

If you want a more intuitive feel of singular and eigenvalue decompositions check out eigshow in MATLAB.

score 10 · Answer 2 · answered Oct 04 '09 at 01:13

10

You can use N = null(A) to get a matrix N. Any of the columns of N (or, indeed, any linear combination of columns of N) will satisfy Ax = 0. This describes all possible such x - you've just found an orthogonal basis for the nullspace of A.

Note: you can only find such an x if A has non-trivial nullspace. This will occur if rank(A) < #cols of A.

answered Oct 04 '09 at 01:13

Peter

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My rank(A) = # cols. How does one "lessen" the value of the rank ? Also null(A) = Empty matrix: 12-by-0. – worbel Oct 04 '09 at 20:04
You should look into low rank approximations. You can use the SVD for this. – Peter Oct 04 '09 at 22:16

score 1 · Answer 3 · edited Oct 21 '09 at 10:34

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You can see if MATLAB has a singular value decomposition in its toolbox. That will give you the null space of the vector.

edited Oct 21 '09 at 10:34

Peter Mortensen

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answered Oct 04 '09 at 02:02

duffymo

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That would be SVD, which results in the same result as null(A). – Jacob Oct 04 '09 at 05:26
They use different numerical methods. – Peter Oct 04 '09 at 10:27
Not really, null(A) uses svd - http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/null.html – Jacob Oct 04 '09 at 15:37
My apologies. I assumed it used the QR algorithm. – Peter Oct 04 '09 at 22:16
I've gone into more detail in my answer – Jacob Oct 05 '09 at 14:50

Miae Kim · Answer 4 · 2016-05-04T15:44:09.103

0

null(A) will give you the direct answer. If you need a nontrivial solution, try reduced row echelon form and refer the first page of the pdf.

R = rref(A)

http://www.math.colostate.edu/~gerhard/M345/CHP/ch7_4.pdf

edited May 04 '16 at 15:44

answered May 04 '16 at 15:38

Miae Kim

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Solving a matrix in MATLAB?

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