Symmetric matrix

Common card · No. 230847

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if a i j {\displaystyle a_{ij}} denotes the entry in the i {\displaystyle i} th row and j {\displaystyle j} th column then Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from ⁠ 2 {\displaystyle 2} ⁠, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a self-adjoint operator represented in an orthonormal basis over a...

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