An orthogonal basis is a set of vectors in a vector space that are mutually orthogonal (perpendicular) to each other and span the space.
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An orthogonal basis of an inner-product vector space consists of nonzero mutually orthogonal vectors that span the space. The orthogonal projection of onto a finite-dimensional span is . Dividing each vector by its norm produces an orthonormal basis. For centered random variables, the inner product is covariance; an orthogonal basis therefore consists of uncorrelated variables, without requiring unit variance.