NormalMatrixQ

NormalMatrixQ[m]

gives True if m is an explicitly normal matrix, and False otherwise.

Details and Options

  • A matrix m is normal if m.ConjugateTranspose[m]ConjugateTranspose[m].m.
  • NormalMatrixQ 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 aij and bij are taken to be equal if f[aij,bij] gives True where a=m.m and b=m.m.
  • For approximate matrices, the option Tolerance->t can be used to indicate that the norm γ=m.m-m.m satisfying γt γ is taken to be zero where γ is the infinity norm of the matrix m.

Examples

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Basic Examples  (1)

Test if a matrix is normal:

In[1]:=
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Out[1]=

Scope  (5)

Options  (2)

Applications  (2)

Properties & Relations  (9)

See Also

HermitianMatrixQ  SymmetricMatrixQ  AntihermitianMatrixQ  AntisymmetricMatrixQ  PositiveSemidefiniteMatrixQ  ConjugateTranspose

Introduced in 2014
(10.0)