**Unitary matrix** A is a unitary matrix if the adjoint of matrix A is equal to the inverse of A:

A

^{†} = A

^{-1} For an inverse matrix A the following relation is true:

AA

^{-1} = A

^{-1}A = 1

It is therefore also true that:

AA

^{†} = A

^{†}A = 1

If A is a real and unitary matrix, then A is said to be orthogonal since A

^{T} = A

^{-1} The adjoint of a matrix is the transpose and complex-conjugate of that matrix. If A is real the complex-conjugate is equal to itself so the adjoint is just the transpose of the matrix.

The unitary matrix is not to be confused with a unit matrix. For a unit matrix A it holds that

**1A** =

**A1** =

**A** and (

**1**)

_{ij} = δ

_{ij} Examples of unit matrixes are:

__See also:__ The adjoint of a matrix

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1200234640 Inverse of a matrix

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1200240564