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