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This algorithm makes it possible to construct, for each list of linearly independent vectors (resp This process simplifies computations and provides geometric insights in vector spaces Basis), a corresponding orthonormal list (resp

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It gives a method for turning a linearly independent list into an orthonormal list with the same span as the original list. When we studied elimination, we wrote the process in terms of matrices and found a = lu It converts a set of linearly independent vectors into a set of orthogonal vectors, which are also normalized to one unit of length.