Linear forms

Linear forms

Dual space

The dual space forms a vector space

Bilinear forms

Bilinear forms

The dot product

Orthogonal vectors

Form-preserving transformations and isometry groups

Orthogonal groups \(O(n, F)\)

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

The Lorentz group

Sesquilinear forms

Sesquilinear forms

Unitary groups \(U(n, F)\)

Inner products

Symmetric matrices

Hermitian (self-adjoint) matrices

Pauli matrices

Positive-definite matrices

Inner products

Cauchy-Schwarz inequality

Multilinear forms and determinants

Multilinear forms

Determinants

Properties of determinants

Determinants of 2x2 and 3x3 matrices

Special groups

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

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

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

Sort

Normal matrices