Conjugate of a matrix is the matrix obtained from matrix ‘P’ on replacing its elements with the corresponding conjugate complex numbers. It is denoted by
Conjugate of a matrix example
Let Q is a matrix such that
Now, to find the conjugate of this matrix Q, we find the conjugate of each element of matrix Q i.e.
This is the conjugate of a 2 x 2 matrix Q.
Conjugate of a matrix properties
The conjugate of matrices P and Q are
If P is a purely imaginary matrix
If P is a real matrix
where ‘a’ is any complex number.