M-matrix

Summary

An M-matrix is a real square matrix of the form $sI - B$, where $B$ is a nonnegative matrix. The number $s$ must be at least the spectral radius of $B$. Since $B$ has no negative entry, the entries of an M-matrix off the diagonal are nonpositive. Such matrices appear when a linear system is discretised, in economic input-output models and in Markov chains. A nonsingular M-matrix has an inverse with all entries nonnegative, so it turns nonnegative data into nonnegative solutions.