44445

Автор(ов):

2

Параметры публикации

Тип публикации:

Статья в журнале/сборнике

Название:

On isomorphisms of pseudo-Euclidean spaces with signature (p,n − p) for p = 2,3

DOI:

10.1016/j.laa.2017.12.003

Наименование источника:

• Linear Algebra and Its Applications

Т. 541

Город:

• Амстердам, Нидерланды

• Elsevier BV

2018

Страницы:

60-80
Аннотация
As is well known, for every orthogonal transformation of the Euclidean space there exists an orthogonal basis such that the matrix of the transformation is block-diagonal with first order blocks ±1and second order blocks that are rotations of the Euclidean plane. There exists a natural generalization of this theorem for Lorentz transformations of pseudo-Euclidean spaces with signature (1, n −1). In addition to invariant subspaces appearing in the Euclidean case, Lorentz transformations can have invariant subspaces of two new types: invariant plane with the Lorenz rotation and 3-dimensional cyclic subspace with isotropic eigenvector and eigenvalue ±1. In this paper, we present similar results about the structure of isomorphisms of pseudo-Euclidean spaces with signature (p, n −p) for p=2, 3.

Библиографическая ссылка:

Павлова Н.Г., Ремизов А.О. On isomorphisms of pseudo-Euclidean spaces with signature (p,n − p) for p = 2,3 // Linear Algebra and Its Applications. 2018. Т. 541. С. 60-80.