Applications of saddle-point determinants

Jan Hauke; Charles R. Johnson; Tadeusz Ostrowski

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 2, page 213-220
  • ISSN: 1509-9415

Abstract

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For a given square matrix A ∈ M n ( 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.

How to cite

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Jan Hauke, Charles R. Johnson, and Tadeusz Ostrowski. "Applications of saddle-point determinants." Discussiones Mathematicae - General Algebra and Applications 35.2 (2015): 213-220. <http://eudml.org/doc/276656>.

@article{JanHauke2015,
abstract = {For a given square matrix $A ∈ M_n(\{ℝ\})$ 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.},
author = {Jan Hauke, Charles R. Johnson, Tadeusz Ostrowski},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {bimatrix game; Mean Value Theorem; optimal mixed strategies; saddle point matrix; value of a game; volumes of simplices},
language = {eng},
number = {2},
pages = {213-220},
title = {Applications of saddle-point determinants},
url = {http://eudml.org/doc/276656},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Jan Hauke
AU - Charles R. Johnson
AU - Tadeusz Ostrowski
TI - Applications of saddle-point determinants
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 2
SP - 213
EP - 220
AB - For a given square matrix $A ∈ M_n({ℝ})$ 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.
LA - eng
KW - bimatrix game; Mean Value Theorem; optimal mixed strategies; saddle point matrix; value of a game; volumes of simplices
UR - http://eudml.org/doc/276656
ER -

References

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  10. [10] MathPages, Heron's Formula and Brahmagupta's Generalization, http://www.mathpages.com/home/kmath196.htm. 
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