I know that for real numbers $\exp(x)$ is defined for every real $x$ and that the result is always greater than zero. I want to compare that to the case $\exp(A)$ where $A$ is a square matrix.
Is it defined for every possible $A$? Does every matrix can be a result of $\exp(A)$?
I have the feeling that every result of $\exp(A)$ is nonsingular but it could be that I only checked specific cases.