Can there be a number to the power of a matrix?

Question

Mathematics

Can there be a matrix in the role of degree?

Answer 1

Except for this, I have never encountered matrix exponentiation. In Hamiltonian systems of linear differential equations, it is possible to take a logarithm (at least by a natural logarithm) of a matrix, which means that there is an action of raising a matrix to a power. Actually it's the same as e^A.

Answer 2

No, It is Immpossible

Answer 3

You can take any differentiable function from the matrix.