I have a matrix $A_{m\times n}$, where $A_j$ , a column of $A$ represents a probability mass function, and so the sum over the column is 1. This is true for all the columns of A, i.e. $\forall j \in \{1,2,...,n\}$, $ \sum_{i \in \{1,2,...m\}} A_{ij}=1$.
I wanted to know if I could use this property in the calculation of the left-pseudo inverse (s.t. $A^{+}A=I$), or if the pseudo-inverse would have any special properties.