The dual space forms a vector space

Form-preserving transformations and isometry groups

Indefinite (pseduo) and split orthognal groups \(O(n,m,F)\)

Hermitian (self-adjoint) matrices

Determinants of 2x2 and 3x3 matrices

Special orthogonal groups \(SO(n, F)\)

Special unitary groups \(SU(n, F)\)

Special linear groups \(SL(n, F)\)