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Matrix-Unitary Matrix

 

Unitary Matrix is a special kind of complex square matrix which has following properties. (U in the following description represents a unitary matrix)

  • U*U = UU* = I (U* is the conjugate transpose of the matrix U)
  • |det(U)| = 1 (It means that this matrix does not have scaling properties, but it can have rotating property)
  • Eigenspaces of U are orthogonal
  • U is diagonalizable
  • U* is unitary
  • U is invertible and the inverse of U is U*
  • The columns of U forms an orthnomal basis
  • The rows of U forms an orthnomal basis
  • The eigenvalues of U lies on the unit circle and they are normal to each other