Applications of saddle-point determinants

Jan Hauke; Charles Johnson; Tadeusz Ostrowski

ArticleOriginal scientific text

Title

Applications of saddle-point determinants

Authors ¹, ², ³

Affiliations

Adam Mickiewicz University, Poznań, Poland
College of William and Mary, Williamsburg, USA
The Jacob of Paradyż University of Applied Sciences, Gorzów Wlkp, Poland

Abstract

For a given square matrix

A \in M_{n} ({ℝ})

and the vector

e \in {(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.

Keywords

ENG

bimatrix game, Mean Value Theorem, optimal mixed strategies, saddle point matrix, value of a game, volumes of simplices

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Title

Applications of saddle-point determinants

Affiliations

Abstract

Keywords

Bibliography