APPLICATIONS OF SADDLE-POINT DETERMINANTS

Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2015, Vol 35, Issue 2

Abstract

For a given square matrix A ∈ Mn(R) and the vector e ∈ (R)^n of ones denote by (A, e) the matrix  A e e^T 0  This is often called the saddle point matrix and it plays a significant role in several branches of mathematics. Here we show some applications of it in: game theory and analysis. An application of specific saddle point matrices that are hollow, symmetric, and nonnegative is likewise shown in geometry as a generalization of Heron’s formula to give the volume of a general simplex, as well as a conditions for its existence.

Authors and Affiliations

Jan Hauke, Charles R. Johnson, Tadeusz Ostrowski

Keywords

Related Articles

GENERALIZED PELL EQUATIONS FOR 2 × 2 MATRICES

In this paper we consider the solutions of the generalized matrix Pell equations X^2 − dY^2 = cI, where X and Y are 2 × 2 matrices over Z, d is a non-zero (positive or negative) square-free integer, c is an arbitrary int...

ALL REGULAR-SOLID VARIETIES OF IDEMPOTENT SEMIRINGS

The lattice of all regular-solid varieties of semirings splits in two complete sublattices: the sublattice of all idempotent regular-solid varieties of semirings and the sublattice of all normal regular-solid varieties o...

Intervals of certain classes of Z-matrices

Let A and B be M-matrices satisfying A ≤ B and J = [A, B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible Mmatr...

Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct

Here we introduce the notion of strong quasi k-ideals of a semiring in SL+ and characterize the semirings that are distributive lattices of t-k-simple(tk-Archimedean) subsemirings by their strong quasi k-ideals. A quasi...

INTRODUCING FULLY UP-SEMIGROUPS

In this paper, we introduce some new classes of algebras related to UPalgebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup,...

Download PDF file
  • EP ID EP304491
  • DOI -
  • Views 36
  • Downloads 0

How To Cite

Jan Hauke, Charles R. Johnson, Tadeusz Ostrowski (2015). APPLICATIONS OF SADDLE-POINT DETERMINANTS. Discussiones Mathematicae - General Algebra and Applications, 35(2), -. https://europub.co.uk/articles/-A-304491