 Symmetric matrix

A real matrix is symmetric when $A^T=A$. It represents a self-adjoint operator in the standard Euclidean inner product.

A symmetric matrix is a square matrix that is equal to its transpose. In mathematical terms, a matrix \( A \) is considered symmetric if: \[ A = A^T \] where \( A^T \) denotes the transpose of the matrix \( A \).

A matrix that equals its transpose:

Can represent a symmetric bilinear form as shown at matrix representation of a symmetric bilinear form, or a quadratic form.