# 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

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topJan 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 -

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