I need to solve linear equation like this:
A*X=B
where A is square and singular.
Any one feasible solution is OK and just what I need.
It is solvable manually but too troublesome if the dimension is high.
So how can I solve such a given equation by tools like MATLAB?
Use pinv function - Moore-Penrose pseudoinverse of matrix.
Consider an example:
A = [1 2 3 4; 5 4 3 2; 0 0 0 1; 0 0 0 2]
x = [1;3;5;7]
b = A*x
Matrix A is singular, so solution by means of mldivide is not satisfactory:
A\b
Warning: Matrix is singular to working precision.
ans =
NaN
NaN
NaN
7
If you use pinv:
pinv(A)*b
ans =
1.0000
3.0000
5.0000
7.0000
Which is equal to the original x.
You can also solve your set of equations by means of least squares method.
Read more:
https://en.wikipedia.org/wiki/Generalized_inverse
Use pinv function - Moore-Penrose pseudoinverse of matrix.
Consider an example:
A = [1 2 3 4; 5 4 3 2; 0 0 0 1; 0 0 0 2]
x = [1;3;5;7]
b = A*x
Matrix A is singular, so solution by means of mldivide is not satisfactory:
A\b
Warning: Matrix is singular to working precision.
ans =
NaN
NaN
NaN
7
If you use pinv:
pinv(A)*b
ans =
1.0000
3.0000
5.0000
7.0000
Which is equal to the original x.
You can also solve your set of equations by means of least squares method.
Read more:
https://en.wikipedia.org/wiki/Generalized_inverse
Dear Grzegorz Knor
When you aplly above question for division of this matrix
but pinv(A)\x gives this error:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 3.469447e-18.
ans =
50.0000
46.0000
227.0000
-96.0000
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