Study of Eigenvalues of Some Matrices via Dilations.

Let A, B be any two positive definite n × n matrices and Y be any n × n matrix. We aim to study the precised estimates of the eigenvalues of M Y (A , B) = A A 1 2 Y B 1 2 B 1 2 Y ⋆ A 1 2 B , with different choices of Y as contractive, expansive or unitary matrix respectively. As applications, we also discuss the block matrices involving several means of the matrices as their entries. [ABSTRACT FROM AUTHOR]