Orthogonal and unitary matrices

A real matrix $A$ is called an orthogonal matrix if its transpose is the same as its inverse, i.e. if $A^T = A^{-1}$ or $A^TA= I$ .

A complex matrix $A$ is called a unitary matrix if its complex conjugate transpose is the same as its inverse, i.e. if $\bar{A}^T = A^{-1}$ or $\bar{A}^TA = I$ . It should be noted that a real unitary matrix is an orthogonal matrix.