nLab linear algebra - contents

linear algebra

Basic concepts

• algebra

• ring, commutative ring

• field, skewfield

• ground ring, ground field

• module, bimodule,

• vector space, basis of a vector space

  rational vector space

  real vector space

  complex vector space

• topological vector space

• linear basis,

  orthogonal basis, orthonormal basis

• linear map, antilinear map

• matrix (square, invertible, diagonal, hermitian, symmetric, row echelon form,…)

• general linear group, matrix group

• eigenspace, eigenvalue

• inner product, Hermitian form

• Gram-Schmidt process

• Hilbert space

• determinant, quasideterminant

• matroid, trace

• Gauss decomposition

• Gauss elimination procedure

• polar decomposition

Theorems

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