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02.1.2. A Particular Symmetric Idempotent Matrix—Solution
Published online by Cambridge University Press: 01 February 2003
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).
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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