UnitaryMatrixQ

UnitaryMatrixQ[m]

gives True if m is a unitary matrix, and False otherwise.

Details and Options

  • A p×q matrix m is unitary if pq and ConjugateTranspose[m].m is the q×q identity matrix, or pq and m.ConjugateTranspose[m] is the p×p identity matrix.
  • UnitaryMatrixQ works for symbolic as well as numerical matrices.
  • The following options can be given:
  • NormalizedTruetest if matrix rows are normalized
    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.
  • For approximate matrices, the option Tolerance->t can be used to indicate that the norm γ=m.m-In satisfying γt is taken to be zero where In is the identity matrix.

Examples

open allclose all

Basic Examples  (1)

Test if a matrix is unitary:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Scope  (4)

Generalizations & Extensions  (1)

Options  (3)

Applications  (5)

Properties & Relations  (10)

See Also

OrthogonalMatrixQ  Orthogonalize  Normalize  SymmetricMatrixQ  HermitianMatrixQ  AntisymmetricMatrixQ  AntihermitianMatrixQ  ConjugateTranspose

Introduced in 2014
(10.0)