Question

State orthonormalisation of a vector​

Answer 1

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Answer 2

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mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product. The Gram–Schmidt process takes a finite, linearly independent set S = {v1, ..., vk} for k ≤ n and generates an orthogonal set S′ = {u1, ..., uk}that spans the same k-dimensional subspace of Rn as S.



The first two steps of the Gram–Schmidt process

The method is named after Jørgen Pedersen Gram and Erhard Schmidt, but Pierre-Simon Laplace had been familiar with it before Gram and Schmidt.[1] In the theory of Lie group decompositions it is generalized by the Iwasawa decomposition.

The application of the Gram–Schmidt process to the column vectors of a full column rankmatrix yields the QR decomposition (it is decomposed into an orthogonal and a triangular matrix).

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