# Matrix exponential function and square root of a matrix

Posted by Mathoman, Wednesday 9 March 2016 at 19:52 - Riddles And Exercises

A little exercice about the matrix exponential made me think abour the following interesting property which makes a link with the sqare root of a matrix. I wish you fun proving ;-)

Let *A* be a real invertible *n*×*n* matrix. One defines

and

Then the set is empty exactly when is.