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based on an earlier version of the Wolfram Language.
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tests whether m is a symmetric matrix.
Test if a matrix is explicitly symmetric:
Test if a matrix is explicitly symmetric:
Click for copyable input
SymmetricMatrixQ works with SparseArray objects:
SymmetricMatrixQ works with symbolic matrices:
Use a different method for symmetric matrices:
Construct real-valued matrices for testing:
For the non-symmetric matrix m, the function just uses Gaussian elimination:
For the symmetric indefinite matrix mi, the function tries the Cholesky method first:
For the symmetric positive definite matrix mp, the function succeeds with the Cholesky method:
Determine if a sparse matrix is structurally symmetric:
For real-valued matrices, a matrix is Hermitian if and only if it is symmetric:
SymmetricMatrixQ[m] is effectively equivalent to m==Transpose[m]:
Real-valued symmetric matrices have all real eigenvalues:
This also means that their characteristic polynomials have real coefficients:
A complex symmetric matrix is not Hermitian:
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