nLab
symmetric matrix
Contents
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 , 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
(…)
Contents
Definition
A square matrix A A symmetric if it is equal to its own transpose matrix : A = A T A = A^T
Symmetric matrices correspond to symmetric bilinear forms . Accordingly a symmetric matrix is called a positive or negative (semi-)definite matrix if the corresponding bilinear form is such (see there ).
References
See also
Last revised on October 19, 2022 at 07:22:58.
See the history of this page for a list of all contributions to it.