Meaning of general linear group | Babel Free

Definitions

For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.

Examples

“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 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.”

“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.”

CEFR level