# THE MOORE-PENROSE INVERSE OF A FREE MATRIX ∗

@article{Britz2007THEMI, title={THE MOORE-PENROSE INVERSE OF A FREE MATRIX ∗}, author={Thomas Britz}, journal={Electronic Journal of Linear Algebra}, year={2007}, volume={16}, pages={19} }

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matrix to that of its Moore-Penrose inverse. Also, it is proved that the bipartite graph or, equivalently…

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