When the conjugate transpose of a complex square matrix is equal to the inverse of itself, then such matrix is called as unitary matrix. If Q is a complex square matrix and if it satisfies Qθ = Q-1 then such matrix is termed as unitary. Please note that Qθ and Q-1 represent the conjugate transpose and inverse of the matrix Q, respectively.
The conjugate transpose of a matrix ‘Q’ can also be written as.
Unitary matrix examples
The example of 2 x 2 unitary matrix is
The example of 3 x 3 unitary matrix is
Note: If A is a unitary matrix then it will satisfy AAθ = I = AθA