= Orthogonal basis
{title2=$\langle u_i,u_j\rangle=0\quad(i\ne j)$}
An <orthogonal basis> of an inner-product <vector space> consists of nonzero mutually <orthogonal vectors> that span the space. The <orthogonal projection> of $v$ onto a finite-dimensional span is $\sum_i\langle v,u_i\rangle u_i/\langle u_i,u_i\rangle$. 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.
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