Inertia of some special matrices.

There have been several articles in literature that study the spectral behaviour of special classes of matrices such as the matrices based on power functiongiven by the matrices, the matricesfor positive values ofrand positive real numbers. Bhatia and Jain in 2015 and Dyn, Goodman and Micchelli in 1986 have studied the spectral behaviour ofand, respectively, for all real values ofr. The power functionis operator monotone whenand operator convex when. It is natural to study the inertia of all these matrices when the power function is replaced by any operator monotone or operator convex function. In the present work, inertia of the matricesandis discussed for non-negative operator monotone and operator convex functionf, which further leads to many known and new results. [ABSTRACT FROM AUTHOR]