A real square matrix is said to be a P-matrix if all its principal minors are positive. It is well known that this property is equivalent to: the nonsign-reversal property based on the componentwiseâ€¦ (More)

Motivated by the similarities between the properties of Z-matrices on Rn + and Lyapunov and Stein transformations on the semidefinite cone S+, we introduce and study Z-transformations on properâ€¦ (More)

A real square matrix Q is a bilinear complementarity relation on a proper cone K in R if x âˆˆ K, s âˆˆ Kâˆ—, and ã€ˆx, sã€‰ = 0â‡’ xQs = 0, where Kâˆ— is the dual of K [14]. The bilinearity rank of K is theâ€¦ (More)

In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.

Motivated by the similarities between the properties of Z-matrices on Rn + and Lyapunov and Stein transformations on the semidefinite cone S+, we introduce and study Z-transformations on properâ€¦ (More)

In this paper, an improved complexity analysis of full Nesterovâ€“Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadraticâ€¦ (More)

(1) If B is a principal submatrix of A, then Ï€(B) â‰¤ Ï€(A) and Î½(B) â‰¤ Î½(A), where Ï€(A) and Î½(A) denote the number of positive and negative eigenvalues of A respectively (and likewise for B); (2) A isâ€¦ (More)

In this paper, using Schur complements, we prove various inequalities in Euclidean Jordan algebras. Specifically, we study analogues of the inequalities of Fischer, Hadamard, Bergstrom, Oppenheim,â€¦ (More)

In this paper, we consider the Schur complement of a subtransformation of a linear transformation defined on the product of two finite dimensional real Hilbert spaces, and in particular, on twoâ€¦ (More)