I'm not a mathematician but the engineering problem I'm considering is more of a mathematical question, that's why I post it here:
Consider the matrices $M$ ($n \times 1$), $T$ ($n \times m$) and $F (m \times 1)$, and: $$ M = TF $$ I solved for $F$ using the Moore-Penrose pseudo inverse. For this special case (where $T$ has full rank), $F$ is simply $$ F = T^+M=T^T (TT^T)^{-1}M $$ with $T^+$ the pseudo-inverse.
However, I want to find only $F \geq 0$. Is there a similar (simple) way to find $F$? Is it a classical problem? There is an infinite amount of solutions $F$, but I want to find $F$ that e.g. minimises the norm of $F$ (like the pseudo-inverse), or e.g. the sum of $F$.
Please let me know if the question is clear or if I need to be more precise