Skip to main content
Log in

Weighted singular decomposition and weighted pseudoinversion of matrices

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For a rectangular real matrix, we obtain a decomposition in weighted singular numbers. On this basis, we obtain a representation of a weighted pseudoinverse matrix in terms of weighted orthogonal matrices and weighted singular numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. G. E. Forsythe and C. B. Moler,Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs 1967.

    MATH  Google Scholar 

  2. C. L. Lawson and R. J. Hanson,Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs 1974.

    MATH  Google Scholar 

  3. R. Bellman,Introduction to Matrix Analysis, McGraw-Hill, New York 1960.

    MATH  Google Scholar 

  4. Kh. D. Ikramov,Problems in Linear Algebra with Generalized Symmetries and Numerical Algorithms for Their Solution [in Russian], Author’s Abstract of the Doctoral Degree Thesis (Physics and Mathematics), Moscow University, Moscow (1991).

    Google Scholar 

  5. I. N. Molchanov and E. F. Galba, “Weighted pseudoinversion of matrices with positive definite weights,” ’sDokl. Akad. Nauk Ukr.SSR, Ser. A, No. 7, 15–17 (1989).

  6. J. F. Ward, T. L. Boullion, and T. O. Lewis, “A note on the oblique matrix pseudoinverse,”SIAM J. Appl. Math.,20, No. 2, 173–175 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  7. R. Penrose, “A generalized inverse for matrices,”Proc. Cambridge Phil. Soc,51, No. 3, 406–413 (1955).

    Article  MATH  MathSciNet  Google Scholar 

  8. L. I. Golovina,Linear Algebra and Some Its Applications [in Russian], Nauka, Moscow 1975.

    Google Scholar 

  9. J. H. Wilkinson,The Algebraic Eigenvalue Problem, Clarendon Press, Oxford 1965.

    MATH  Google Scholar 

  10. G. H. Golub and W. Kahan, “Calculating the singular values and pseudoinverse of a matrix,”SIAM J. Numer. Anal. Ser. B.,2, No. 3, 205–224 (1965).

    Article  MathSciNet  Google Scholar 

  11. G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,”Numer. Math.,14, No. 3, 403–420 (1970).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galba, E.F. Weighted singular decomposition and weighted pseudoinversion of matrices. Ukr Math J 48, 1618–1622 (1996). https://doi.org/10.1007/BF02377829

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02377829

Keywords

Navigation