Skip to main content
Log in

Optimally Conditioned Block 2 × 2 Matrices

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

This paper provides a description of block 2 × 2 Hermitian positive-definite matrices that are optimally conditioned with respect to block diagonal similarity transformations. Bibliography: 7 titles.

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.

Similar content being viewed by others

REFERENCES

  1. H. Bart, I. Gohberg, M. Kaashoek, and P. Van Dooren, “Factorizations of transfer functions," SIAM J. Contr. Optimiz., 18, 675–696 (1980).

    Google Scholar 

  2. J. Demmel, “The condition number of equivalence transformations that block diagonalize matrix pencils," In: Matrix Pencils (B. Kagström and A. Ruhe, eds.), Lecture Notes in Mathematics, 973, Springer (1982), pp. 2–16.

  3. S. C. Eisenstat, J. W. Lewis, and M. H. Schultz, “Optimal block diagonal scaling of block 2-cyclic matrices," Linear Algebra Appl., 44, 181–186 (1982).

    Google Scholar 

  4. L. Elsner, “A note on optimal block scaling of matrices," Numer. Math., 44, 127–128 (1984).

    Google Scholar 

  5. L. Yu. Kolotilina, “Eigenvalue bounds and inequalities using vector aggregation of matrices," Linear Algebra Appl., 271, 139–167 (1998).

    Google Scholar 

  6. M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston (1964).

    Google Scholar 

  7. Song-Gui Wang and Wai-Cheung Ip, “A matrix version of the Wielandt inequality and its applications to statistics," Linear Algebra Appl., 296, 171–181 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolotilina, L.Y. Optimally Conditioned Block 2 × 2 Matrices. Journal of Mathematical Sciences 114, 1794–1802 (2003). https://doi.org/10.1023/A:1022402502491

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022402502491

Keywords

Navigation