Dictionary

general linear group en · NOUN

Meanings

1. For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.
   • 1993, Peter J. Olver, Applications of Lie Groups to Differential Equations, Springer, 2000, Softcover Reprint, page 17, Often Lie groups arise as subgroups of certain larger Lie groups; for example, the orthogonal groups are subgroups of the general linear groups of all invertible matrices.
   • We show how to put a Lie group structure on a closed subgroup of the general linear group and determine the Lie algebras of the classical groups. 2009, Roe Goodman, Nolan R. Wallach, Symmetry, Representations, and Invariants, Springer, page 1:
   • We will again call this group the general linear group and denote it by GL₃. In just the same way, the set of all nonsingular linear transformations of the plane L₂ is a group denoted by GL₂ and called the general linear group of order two. 2003, Maks Aizikovich Akivis, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 119:

Forms

Deriveds

projective general linear group

Relateds

matrix group · Lie group · linear group · special linear group

Translations (1)

pl pełna grupa liniowa (group of invertible n×n matrices)