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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 $A$ is called symmetric if it is equal to its own transpose matrix : $A = A^T$ .

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.