High Quality Content by WIKIPEDIA articles! In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1,...,vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u1,...,uk} that generate the same subspace as the vectors v1,...,vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span. In addition, if we want the resulting vectors to all be unit vectors, then the procedure is called orthonormalization. Colloquially, orthogonalization is the process of splitting a problem or system into its distinct components.

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