Examples of groups

General linear group

The general linear group is the automorphism group of the vector space in . When dealing with matrices, the notation refers to invertible matrices over the field . Of particular importance is the Complex general linear group and its subgroup Real general linear group.

Properties

• Matrix determinant is a homomorphism

Related groups

• A subgroup is the Special linear group, which can be defined as the Kernel of a group homomorphism of the Matrix determinant.
• Centre of the general linear group consists of scalar matrices and is isomorphic to the multiplicative group .
• Projective general linear group

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