nLab higher linear algebra - contents

linear algebra, higher linear algebra

Ingredients

• algebra, higher algebra,

• homological algebra, stable homotopy theory

Basic concepts

• ring, A-∞ ring

• commutative ring, E-∞ ring

• module, ∞-module, (∞,n)-module

• field, ∞-field

• vector space, 2-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, …)

• general linear group, matrix group

• eigenspace, eigenvalue

• inner product, Hermitian form

  Gram-Schmidt process

• Hilbert space

Theorems

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