High Quality Content by WIKIPEDIA articles! In linear algebra, a symmetric matrix is a square matrix, A, that is equal to its transpose. A real symmetric matrix represents a self-adjoint operator over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is generally assumed that a symmetric matrix refers to one which has has real-valued entries. Symmetric matrices appear naturally in a variety of applications, and typical numerical linear algebra software makes special accommodations for them.

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