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Factorization of the Matrix of Orthogonal Projector on a Subspace

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A deep factorization of the orthogonal projection matrix onto a subspace is obtained. The LQ decomposition is used. For construction of an orthogonal matrix Q the method of successive rank reduction is applied.

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References

  1. V. N. Malozemov, Linear Algebra without Determinants. Quadratic Function [in Russian], SPbU, St.Petersburg (1997).

  2. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge Univ. Press, Cambridge (1985).

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  3. G. H. Golub and C. F. Van Loan, Matrix Computations, (4th ed.) Johns Hopkins Univ. Press, Baltimore and London (2013).

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  4. Lineal. Basic Electronic Encyclopedia of Linear Algebra [in Russian], http://lineal.guru.ru/http://lineal.guru.ru/

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Authors and Affiliations

  1. St.Petersburg State University, St. Petersburg, Russia

    V. N. Malozemov

  2. St.Petersburg State University, Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    G. Sh. Tamasyan

Authors
  1. V. N. Malozemov
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  2. G. Sh. Tamasyan
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Corresponding author

Correspondence to V. N. Malozemov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 499, 2021, pp. 67–76.

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Malozemov, V.N., Tamasyan, G.S. Factorization of the Matrix of Orthogonal Projector on a Subspace. J Math Sci 273, 485–491 (2023). https://doi.org/10.1007/s10958-023-06515-w

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  • DOI: https://doi.org/10.1007/s10958-023-06515-w

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