Examples of groups

General linear group

The general linear group $G L (𝑉)$ is the automorphism group of the vector space $𝑉$ in $𝖵 𝖾 𝖼 𝗍 𝕂$ . When dealing with matrices, the notation $G L 𝑛 (𝕂)$ refers to invertible $𝑛 \times 𝑛$ matrices over the field $𝕂$ . Of particular importance is the Complex general linear group and its subgroup Real general linear group.

Properties

Matrix determinant is a homomorphism

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 $𝕂 \times$ .
Projective general linear group

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