I have a matrix from which I have to find the pseudoinverse, but none of the methods that I found gave me the correct answer (one that Wolfram Alpha gave me).
The matrix is:
$$ \pmatrix{0 & 1 & 0\cr1 & 0 & 0\cr} $$
I would be really thankful if someone could help me :)
Your matrix $A = \pmatrix{0 & 1 & 0\cr1 & 0 & 0\cr}$ is almost in the form of the singular-values matrix already, you just have to interchange the rows. So $A = U \Sigma V^T$ where $$ U = \pmatrix{0 & 1\cr 1 & 0\cr}, \ \Sigma = \pmatrix{1 & 0 & 0\cr 0 & 1 & 0\cr}, \ V = \pmatrix{1 & 0 & 0\cr 0 & 1 & 0\cr 0 & 0 & 1\cr}$$ Then $\Sigma^+ = \Sigma^T$, and the pseudo-inverse is $A^+ = V \Sigma^+ U^T$.