In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication...

especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced...

multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant det : GL ⁡ ( n , R ) → R ×...

groups). A group G is said to be linear if there exists a field K, an integer d and an injective homomorphism from G to the general linear group GLd (K)...

translations, and the affine group of A can be described concretely as the semidirect product of V by GL(V), the general linear group of V: Aff ⁡ ( V ) = V ⋊...

mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to...

orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally...

similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore the same as conjugacy, and similar matrices...

of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of the general linear group GL(n,...

construction of the unitary group from the general linear group. The unitary group arises as follows: the general linear group over the complex numbers has...