Transpose Conjugate of a Matrix:

The transpose of the conjugate of a matrix A is known as transposed conjugate of A and is shown by A^θ. The conjugate of the transpose of A is similar as the transpose of the conjugate of A i.e.  = A^θ

If A = [a_ij]_mxn, then A^θ = [b_ji]_nxm  where b_ji = 

i.e. the (j, i)^th component of A^θ= the conjugate of (i, j)^th components of A.

For example:  If A = 

Properties of Transpose conjugate:

(i).        (A^θ)^θ = A

(ii).       (A + B)^θ  = A^θ + B^θ

(iii).      (kA)^θ =  A^θ, k being any natural number

(iv).      (AB)^θ = B^θA^θ

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