nLab
elementary matrix
Redirected from "elementary matrices".
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
An elementary matrix is a square matrix which is obtained from the identity matrix by performing one row operation, that is either
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interchanging two rows (in which case it is a permutation matrix),
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rescaling the row by multiplying it with a nonzero element,
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or adding a multiple of one row to some other row.
References
See also:
Last revised on January 30, 2026 at 15:33:53.
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