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A note on semidirect sum of Lie algebras

100%

Ostrowski T.

Discussiones Mathematicae - General Algebra and Applications

2013

tom 33

nr 2

233-247

In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.

Applications of saddle-point determinants

51%

Hauke J., Johnson C., Ostrowski T.

Discussiones Mathematicae - General Algebra and Applications

2015

tom 35

nr 2

213-220

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.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

2 Ostrowski T.

1 Hauke J.

1 Johnson C.

1 2015

1 2013

Wyniki wyszukiwania

A note on semidirect sum of Lie algebras

Applications of saddle-point determinants