0
$\begingroup$

How can I prove that the left pseudo-inverse of matrix $A$ is $A^{\dagger}_l = (A^TA)^{-1}A^T,$

I know that this is true only if $\mathrm{rank}(A)=n$. and that if $\mathrm{rank}(A)=n$ that means that $A^TA$ is invertible.

I also proved that $A^{\dagger}_lA =I$

I tried to play with multiplying the matrices but it didn't help...

  • 0
    So... you proved it right? I don't think I understand what you are asking, since it seems like you proved what you are trying to prove.2014-12-13

1 Answers 1

1

Actually $A^{\dagger}_l = (A^TA)^{-1}A^T$ is just A left inverse of $A$, $(A^TMA)^{-1}A^TM$ is also the left inverse for any matrix $M$ such that $A^TMA$ is invertible.