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02.1.2. A Particular Symmetric Idempotent Matrix—Solution

Published online by Cambridge University Press:  01 February 2003

George P.H. Styan  and
Hans Joachim Werner
George P.H. Styan
Affiliation:
McGill University, Montreal
Hans Joachim Werner
Affiliation:
University of Bonn
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Extract

It is easy to see that Problem 02.1.2 holds more generally in that the result is valid for B Hermitian complex (rather than “symmetric real”), for m = 0,1,…,q (rather than just for “m < q”), for r ≠ 0 (rather than just for “integer r > 1”), and for tr(Bk) = tr(Ck), k = 1,2,3,4 (rather than for “k = 1,2,…”), as shown by Shanbhag (1970).

Type
PROBLEMS AND SOLUTIONS
Information
Econometric Theory , Volume 19 , Issue 1 , February 2003 , pp. 227 - 228
Copyright
© 2003 Cambridge University Press

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Footnotes

Excellent solutions were independently proposed by G. Dhaene, J. Hill, S. Lawford and C. Dehon, P. Omtzigt, G. Trenkler, M. Van de Velden, D. Wiens, and H. Neudecker (the poser of the problem).

References

REFERENCES

Lancaster, P. (1969) Theory of Matrices. New York: Academic Press.
Shanbhag, D.N. (1970) On the distribution of a quadratic form. Biometrika 57, 222–223.Google Scholar