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Two vectors and are said to be orthonormal if they are both orthogonal and normalized. A set of vectors which are pairwise orthonormal is called an orthonormal set.

When referring to functions, usually the L²-norm is assumed unless otherwise stated, so that two functions and are orthonormal over the interval if

Unfortunately, the word normal is sometimes used synonymously with orthogonal.

See also: normalized vector, orthogonal, Lp space.