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Orthogonalisation of vectors

Matrix decompositions and approximation problems

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Suggested Reading

  1. A detailed discussion of the polar and the QR deompositions may be found in H Helson, Linear Algebra, TRIM 4, Hindustan Book Agency, 1994.

  2. A more advanced treatment of matrix approximation problems may be found in R Bhatia, Matrix Analysis, Springer-Verlag, 1997.

  3. The relevance of matrix approximation problems to quantum chemistry is explained in the article by J A Goldstein and M Levy, Linear algebra and quantum chemistry, American Math. Monthly, 78, 710–718, 1991.

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  4. The Löwdin Orthogonalisation was proposed by P O Löwdin, On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals, J. Chem. Phys., 18, 365–374, 1950.

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  5. Algorithms for finding the QR and the Singular Value Decompositions are discussed in G Golub and C Van Loan, Matrix Computations, The Johns Hopkins University Press, 1983.

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  1. Indian Statistical Institute, 7, SJS Sansanwal Marg, 110 016, New Delhi, India

    Rajendra Bhatia

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  1. Rajendra Bhatia
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Bhatia, R. Orthogonalisation of vectors. Reson 5, 52–59 (2000). https://doi.org/10.1007/BF02838999

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