The Dual of the Cone of All Convex Functions on a Vector Space. (Short Communication).
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
Given a graph , if there is no nonisomorphic graph such that and have the same signless Laplacian spectra, then we say that is -DS. In this paper we show that every fan graph is -DS, where and .
The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.