Orthogonal matrices with determinant 1 form a subgroup called "special orthogonal group". This expression highlights the relation between unitary matrices and orthogonal matrices of angle . A basis for consisting of mutually orthogonal unit vectors is called an orthonormal basis. The trough is parabolic along one axis and linear in the orthogonal axis. It consists of all orthogonal matrices of determinant . It is similarly additive for orthogonal polarizations. To measure closeness, we may use any matrix norm invariant under orthogonal transformations. There is saving of bandwidth by using multicarrier modulation with orthogonal frequency division multiplexing. In general, transverse waves occur as a pair of orthogonal polarizations. The complex analogue of an orthogonal matrix is a unitary matrix. This means formula 30 and formula 31 are orthogonal vectors. Now, formula 96 because they are spanned by vectors corresponding to orthogonal spaces. Both and form a sequence of orthogonal polynomials. The Pythagorean identity can be extended to sums of more than two orthogonal vectors. Start with a set of vectors that are mutually orthogonal.