I just wanted to ask you whether a theorem that I have found on wikipedia is correct! I have found a theorem that says, that a matrix is positive definite if and only if it is equal to the product of a matrix and its adjoint matrix. But clearly the product of a matrix and its adjoint matrix is self adjoint, does this mean that each positive definite matrix is self-adjoint?
I don't know what is the definition of the positive matrix. But if the matrix can be treated as a operator,the answer is right. Each positive matrix is self-adjoint. You can know some details in the book-----A Course in Functional Analysis(Author:John B.Conway),page 240-241.