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{wiki=Symmetric_matrix}

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 \$.


Symmetric matrix

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


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A <matrix> that equals its <transpose>:
$$
M = M^T
$$

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


Symmetric matrix

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Symmetric matrix

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