On isomorphisms of pseudo-Euclidean spaces with signature (p,n − p) for p = 2,3статья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 26 февраля 2018 г.
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 ±1 and 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.