which implies that A is a square matrix. Intuitively, the entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right). Example:
Any diagonal matrix is symmetric, since all its offdiagonal entries are zero.
One of the basic theorems concerning such matrices is the finitedimensional spectral theorem, which says that any symmetric matrix whose entries are real can be diagonalized by an orthogonal matrix.
See also skewsymmetric matrix.
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