Geometric series of matrix

284 Views Asked by At

We know that $$I+M+M^2+\cdots$$ is convergent iff $\rho(M)<1$.

And if it is convergent then it coverges to $(I-M)^{-1}$

Doubts If all entries of $M$ are positive then I feel that all entries of $(I-M)^{-1}$ should also be positive. But In actual this need not true. Please help me