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.
+5
A:
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.
Peter
2009-10-04 01:13:05
My rank(A) = # cols. How does one "lessen" the value of the rank ? Also null(A) = Empty matrix: 12-by-0.
srand
2009-10-04 20:04:01
You should look into low rank approximations. You can use the SVD for this.
Peter
2009-10-04 22:16:44
+1
A:
You can see if MATLAB has a singular value decomposition in its toolbox. That will give you the null space of the vector.
duffymo
2009-10-04 02:02:39
Not really, null(A) uses svd - http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/null.html
Jacob
2009-10-04 15:37:01
+2
A:
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.
Jacob
2009-10-05 14:56:07