SymmetricMatrixQ

SymmetricMatrixQ[m]

gives True if m is explicitly symmetric, and False otherwise.

Details and Options

  • A matrix m is symmetric if m==Transpose[m].
  • SymmetricMatrixQ works for symbolic as well as numerical matrices.
  • The following options can be given:
  • SameTestAutomaticfunction to test equality of expressions
    ToleranceAutomatictolerance for approximate numbers
  • For exact and symbolic matrices, the option SameTest->f indicates that two entries mij and mkl are taken to be equal if f[mij,mkl] gives True.
  • For approximate matrices, the option Tolerance->t can be used to indicate that all entries Abs[mij]t are taken to be zero.
  • For matrix entries Abs[mij]>t, equality comparison is done except for the last bits, where is $MachineEpsilon for MachinePrecision matrices and for matrices of Precision .

Examples

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Basic Examples  (1)

Test if a matrix is explicitly symmetric:

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Out[1]=
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Scope  (5)

Options  (2)

Applications  (12)

Properties & Relations  (8)

Possible Issues  (1)

Neat Examples  (1)

See Also

AntisymmetricMatrixQ  HermitianMatrixQ  AntihermitianMatrixQ  PositiveSemidefiniteMatrixQ  Transpose  SymmetrizedArray  Symmetrize

Introduced in 2008
(7.0)
| Updated in 2014
(10.0)