**The adjoint of a matrix** The adjoint of a matrix is the transpose and conplex-conjugate of a matrix. Synonyms: conjugate transpose, Hermitian transpose, adjoint matrix

Given a matrix A, the matrix A

^{T} is the transpose of A if A(i,j) = A

^{T}(j,i).

The complex-conjugate of a complex number z=a+bi is z=a-bi (where a and b are real numbers).

The complex-conjugate of a matrix is a matrix for which all elements A(i,j) are replaced by their complex-conjugates (A(i,j))

^{*} The adjoint of a matrix A is denoted as A

^{†} For a product of two matrices A and B it is found that:

(AB)

^{†} = B

^{†}A

^{†} __See also:__ Conjugate transpose

http://en.wikipedia.org/wiki/Conjugate_transpose