When solving linear problems, there are many different ways of assessing if $Ax=b$ has a unique solution for a given $A$ by looking at properties of $A$ like the rank or singular values. If I am solving the non-negative least squares version, where $x_i \geq 0$ with the additional constraint that my $a_{ij}\geq 0$, are there any equivalent techniques?
The NNLS regime feels qualitatively different than the unconstrained version because while two columns in $A$ cannot "cancel" each other out (as you can't subtract one from the other, as again the $x_i$ are positive) you could still have a matrix with a duplicate column, or where the (positive) sum of two columns is equal to a third column.
This problem arises in inverse problems in imaging but I have struggled to find any good references or solutions.