nLab
elementary matrix
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
Am elementary matrix is a square matrix which is obtained from the identity matrix by performing one row operation, that is either

interchanging two rows (in which case it is a permutation matrix),

rescaling the row by multiplying it with a nonzero element,

or adding a multiple of one row to some other row.
References
See also:
Last revised on May 21, 2024 at 13:11:11.
See the history of this page for a list of all contributions to it.