 Gram–Schmidt process

The Gram-Schmidt process replaces linearly independent vectors $v_1,\dots ,v_n$ by orthogonal vectors with the same successive spans, subtracting from each $v_k$ its projections onto the preceding vectors.

The Gram–Schmidt process is an algorithm used in linear algebra to orthogonalize a set of vectors in an inner product space, most commonly in Euclidean space. The primary goal of this process is to take a finite, linearly independent set of vectors and transform it into an orthogonal (or orthonormal) set of vectors, which are mutually perpendicular to one another or normalized to have unit length.