nLab
matrix decomposition
Context
Linear algebra
linear algebra, higher linear algebra
Ingredients
Basic concepts

ring, A∞ ring

commutative ring, E∞ ring

module, ∞module, (∞,n)module

field, ∞field

vector space, 2vector 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
GramSchmidt process

Hilbert space
Theorems
(…)
Contents
Idea
Under matrix decomposition one understands the factoring of matrices as products of matrices of a certain form.
This may and often is also referred to as matrix factorization, which however also has other meanings.
Examples
References
Relation of matrix decompositions to flows of integrable systems:
 P. Deift, L. C. Li, C.Tomei, Matrix factorizations and integrable systems, Commun. Pure Appl. Math. 42 4 (1989) 443521 [doi:10.1002/cpa.3160420405]
Last revised on June 17, 2024 at 17:42:02.
See the history of this page for a list of all contributions to it.