What does it mean when a matrix is to the (-1/2) power?

Question

I'm reading a machine learning paper that uses a form of matrix normalization called symmetric divisive; given a matrix A and a diagonal matrix D derived from A, we define $$N=D^{-1/2}AD^{-1/2}$$ I am not sure what that exponent means, am I supposed to invert and then take the square root of the matrix? Of its values? A little lost here.

Answer 1

Just for future reference, here is a general way of finding integer and non-integer powers of a square matrix.

The theorem is

$$If \ \ A\vec{v} = \lambda\vec{v} \ ,\\ A^n\vec{v} = \lambda^n\vec{v}$$

where $\lambda$ is an eigenvalue for the eigenvector $\vec{v}$ of matrix $A$.

Source, Examples and Further Information : http://www.blackmesapress.com/Eigenvalues.htm