# Conjugate Transpose of a Matrix – Example & Properties

Conjugate transpose of a matrixP’ is basically a matrix which is equal to the conjugate of the matrix obtained by taking the transpose of the matrixP’. In order to find the conjugate transpose of any matrix; firstly, transpose is obtained and secondly, the conjugate is obtained. The conjugate transpose is generally denoted as Contents
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## Conjugate transpose of a matrix example

Let P is a matrix such that Now, to find the conjugate transpose of this matrix P, we first find the transpose of matrix P i.e. In the second step, we find conjugate of the matrix PT This is the conjugate transpose of a 2 x 2 matrix P.

## Conjugate transpose of a matrix properties

The conjugate transpose of matrices S and R are Sθ and Rθ, respectively. Then,

1. (Sθ)θ = S and (Rθ)θ = R

2. (S + R)θ = Sθ + Rθ where ‘a‘ is a complex number.

4. (SR)θ = RθSθ

The conjugate transpose is used to check special complex matrices i.e. hermitian matrix, skew hermitian matrix and unitary matrix.

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