# What is Unitary Matrix? Example

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

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