NormalMatrixQ

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

Details and OptionsDetails 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.
Introduced in 2014
(10.0)