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Orthogonal and oblique projectors and the characteristics of pairs of vector spaces

Published online by Cambridge University Press:  24 October 2008

S. N. Afriat
S. N. Afriat
Affiliation:
Department of MathematicsThe Hebrew UniversityJerusalem
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Extract

The statistical operation of multiple linear regression by least squares is equivalent to the orthogonal projection of vectors of observations on a space spanned by vectors of observations; and a partial regression can be similarly represented as an oblique projection. This connexion between a statistical and a formal algebraical operation gives the main source of interest for this investigation. Its object is to develop algebraical theory which supplies terms necessary for a unified algebraical and geometrical formulation of concepts in multivariate analysis. An exposition of the statistical theory is to be made in a separate paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 4 , October 1957 , pp. 800 - 816
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Hamburger, H. L. and Grimshaw, M. E.Linear transformations in n-dimensional vector space (Cambridge, 1951).Google Scholar
(2)Halmos, P.Finite-dimensional vector spaces (Princeton, 1948).Google Scholar
(3)Afriat, S. N.On the latent vectors and characteristic values of products of pairs of symmetric idempotents. Quart. J. Math. (2), 7 (1956), 76–8.CrossRefGoogle Scholar
(4)Hotelling, H.Relations between two sets of variates. Biometrika, 28 (1935), 321–77.CrossRefGoogle Scholar