Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T04:10:23.162Z Has data issue: false hasContentIssue false
  • English
  • Français

Solutions to Problems Posed in Volume 20(1) and 20(2): 04.2.1. A Range Equality for Block Matrices with Orthogonal Projectors—Solution

Published online by Cambridge University Press:  31 March 2005

Hans Joachim Werner
Hans Joachim Werner
Affiliation:
University of Bonn, Germany
Get access Rights & Permissions [Opens in a new window]

Extract

This solution offers additional insights into the theory of block-tridiagonal Toeplitz matrices. Block Toeplitz matrices have constant blocks on each block diagonal parallel to the block main diagonal. A block partitioned matrix is said to be block-tridiagonal if the nonzero blocks occur only on the block subdiagonal, the block main diagonal, and the block superdiagonal. Block-tridiagonal Toeplitz matrices are particularly nice in that they are inexpensive to investigate. Our first observation on such particular block Toeplitz matrices is easy to check, and its proof is therefore left to the reader.

Type
SOLUTIONS TO PROBLEMS
Information
Econometric Theory , Volume 21 , Issue 2 , April 2005 , pp. 485 - 487
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Excellent solutions have been proposed independently by Geert Dhaene (Katholieke Universiteit, Leuven, Belgium), Dietmar Bauer (Technische Universität, Wien, Austria), and Yongge Tian (Queens University, Canada), the poser of the problem.

References

REFERENCES

Tian, Y. (2003) A range equality for block matrices. IMAGE, The Bulletin of the International Linear Algebra Society 31, 44.Google Scholar
Werner, H.J. (1985a) More on BLU estimation in regression models with possibly singular covariances. Linear Algebra and Its Applications 67, 207–214.Google Scholar
Werner, H.J. (1985b) Weak complementarity and missing observations. Methods of Operations Research 50, 421–439.Google Scholar
Werner, H.J. (1986) Generalized inversion and weak bi-complementarity. Linear and Multilinear Algebra 19, 357–372.Google Scholar
Werner, H.J. (1987) C. R. Rao's IPM method: A geometric approach. In M.L. Puri, J.P. Vilaplana, & W. Wertz (eds.), New Perspectives in Theoretical and Applied Statistics, pp. 367–382. Wiley.
Werner, H.J. (2003) Product of two Hermitian nonnegative definite matrices. Solution 29-5.4. IMAGE, The Bulletin of the International Linear Algebra Society 30, 25.Google Scholar