1To obtain the square root of a matrix, say matrix C  , follow these steps.

  1. Determine the eigenvalues λ  of the matrix.
  2. For each eigenvalue λn  determine the correspending eigenvector Vn
  3. Construct the Matrix N  whose columns are the eigenvectors Vn  . i.e. the first column will be the vector V1  etc...
  4. Construct matrix M  with diagonal elements that contains the √ λn-  . i.e. M (1,1)= √ λ1  , M (2,2)= √λ2  , and so forth. (This is the Jordan form for real distinct eigenvalues)
  5. Now √C-= NT MN

In Matlab, the command expm() can be used to calculate sqrt of a matrix.