I am trying to find out how to get the error associated with with this equation G = MD
where I compute the pseudo-inverse of D and left multiply by G to get M.
Thanks
I am trying to find out how to get the error associated with with this equation G = MD
where I compute the pseudo-inverse of D and left multiply by G to get M.
Thanks
The Moore-Penrose pseudo-inverse of $D$ is a matrix $D^+$ such that $D D^+ D = D$. If the "error" is $E = M - G D^+ $, this says $E D = 0$, i.e. $E$ annihilates the column space of $D$. On the other hand, $E v = M v$ for $v \in \text{Ker} D^*$, i.e. vectors orthogonal to the column space of $M$.