Given eigen values for a matrix in n dimension how one can generate a corresponding covariance matrix which result in having those eigen values

Question

I am having some difficulties resolving this: Given eigen values for a matrix in n dimension how one can generate a corresponding covariance matrix which result in having those eigen values.

Any advice is much appreciated.

Ali

Answer 1

Take any orthogonal matrix R and construct

covariance = R*diag(eigenvalues)*R'