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**sandipdas76** i have a matrix a which is positive definite and having all real elements. A can have multiple eigenvalues but it is not defective.

I want to get a similar matrix b (i.e., b has the same eigenvalues as a) which is symmetric and real. So precisely i want to construct a nonsingular matrix x such that b = inv(x) a x.

So it will be extremely helpful if anyone can tell me how to get such x or at least give me some reference.

Alternatively:

A method is available to get a symmetric similar matrix for a from another nonsingular symmetric matrix y if it satisfies a y = y a_tr. But such similar matrix obtained from y will only be real if y is positive definite. So alternatively, any help in getting a positive definite y for given a will be extremely useful.