nLab
matrix decomposition
Context
Linear algebra
linear algebra, higher linear algebra
Ingredients
Basic concepts
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ring, A-∞ ring
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commutative ring, E-∞ ring
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module, ∞-module, (∞,n)-module
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field, ∞-field
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vector space, 2-vector space
rational vector space
real vector space
complex vector space
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topological vector space
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linear basis,
orthogonal basis, orthonormal basis
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linear map, antilinear map
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matrix (square, invertible, diagonal, hermitian, symmetric, …)
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general linear group, matrix group
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eigenspace, eigenvalue
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inner product, Hermitian form
Gram-Schmidt process
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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) 443-521 [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.