Singular values, diagonal elements, and extreme matrices

Diagonals and Partial Diagonals of Sum of Matrices

“…Furthermore, some convexity properties of the joint orbits are considered. These extend many results in matrix inequalities, and answer some questions raised by Miranda [7] (see Theorem 2.7).…”

“…This result was later extended to the product of matrices as follows, see [8], [7], [15]. It is interesting that the same conditions (2.2) and (2.3) are necessary and sufficient in the extended result with a simple (natural) modification of the definition for s 1 , .…”

“…, A k ) defined as in (2.1). In fact, the problem was raised explicitly in [7]. .3) may not be necessary, as shown in the following example.…”

Cases of equality for certain inequalities involving a G-doubly stochastic map

“…Our aim is to find necessary and sufficient conditions for those inequalities to become equalities. Many authors obtained such conditions for various maps defined on linear spaces equipped with the classical majorization or the weak majorization (e.g., see [4,10,11,13,14,18]). However, very little is known about such conditions for a generic G-doubly stochastic map on a space supplied with a G-majorization preordering.…”