Estimates for the eigenvalues of the Jordan product of Hermitian matrices (Q793817)

For Hermitian \(n\times n\)-matrices A and B the Jordan product is defined as the Hermitian matrix \(C=AB+BA\). For positive definite A and B this article gives necessary conditions for the i-th eigenvalue \(c_ i\) of C to be nonnegative and derives a lower bound on \(c_ i\) in terms of suitable eigenvalues of A and B.