Principal component analysis : some majorisation, perturbation and nonnegative matrix theory

Frank Critchley

Statistique et analyse des données (1988)

  • Volume: 13, Issue: 1, page 8-14
  • ISSN: 0750-7364

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Critchley, Frank. "Principal component analysis : some majorisation, perturbation and nonnegative matrix theory." Statistique et analyse des données 13.1 (1988): 8-14. <http://eudml.org/doc/108961>.

@article{Critchley1988,
author = {Critchley, Frank},
journal = {Statistique et analyse des données},
language = {eng},
number = {1},
pages = {8-14},
publisher = {Association pour la statistique et ses illustrations},
title = {Principal component analysis : some majorisation, perturbation and nonnegative matrix theory},
url = {http://eudml.org/doc/108961},
volume = {13},
year = {1988},
}

TY - JOUR
AU - Critchley, Frank
TI - Principal component analysis : some majorisation, perturbation and nonnegative matrix theory
JO - Statistique et analyse des données
PY - 1988
PB - Association pour la statistique et ses illustrations
VL - 13
IS - 1
SP - 8
EP - 14
LA - eng
UR - http://eudml.org/doc/108961
ER -

References

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  1. [1] BERMAN, A. and PLEMMONS, R.J., (1979), Non-negative matrices in the mathematical sciences, London: Academic Press. Zbl0484.15016MR544666
  2. [2] CRITCHLEY, F., (1983), The Euclideau structure of a dendrogram, Warwick Statistics Research Report No. 48. 
  3. [3] CRITCHLEY, F., (1985), Influence in principal components analysis, Biometrika, Vol. 72, pp. 627-636. Zbl0608.62068MR817577
  4. [4] FAN, K., (1949) and ( 1950), On a theorem of Weyl concerning eigenvalues of linear transformations I and II, Proc. Nat. Acad. Sci. U.S.A., Vol. 35, pp. 652-655 and Vol. 36, pp.31-35. Zbl0041.00602MR34519
  5. [5] FROBENIUS, G., (1908) and ( 1909), Über Matrizen aus positiven Elementen I and II, S.-B. Preuss. Akad. Wiss. (Berlin), pp. 471-476 and 514-518. Zbl39.0213.03JFM40.0202.02
  6. [6] HOPH, E., (1963), An inequality for positive integral linear operators, J. Math. and Mech., Vol. 12, pp. 683-692. Zbl0115.32501MR165325
  7. [7] HORN, A., (1954), Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math., Vol. 76, pp. 620-630. Zbl0055.24601MR63336
  8. [8] KENDALL, M.G. (1975), Multivariate analysis, London: Griffin. Zbl0551.62032
  9. [9] MARSHALL, A.W. and OLKIN, I., (1979), Inequalities: theory of majorization and its applications, London: Academic Press. Zbl0437.26007MR552278
  10. [10] MIRSKY, L., (1958), Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc, Vol. 33, pp. 11-21. Zbl0101.25303MR91931
  11. [11] MORRISON, D.F., (1976), Multivariate statistical methods, London: McGraw-Hill. Zbl0355.62049MR408108
  12. [12] OSTROWSKI, A.M. (1963), On positive matrices, Math. Annalen. Vol. 150, pp. 276-284. Zbl0115.24803MR148680
  13. [13] PERRON, O. (1907), Zur Theorie der Über Matrizen, Math. Ann., Vol. 64, pp. 248-263. Zbl38.0202.01MR1511438JFM38.0202.01
  14. [14] RAO, C.R., (1973), Linear statistical inference and its applications, London: John Wiley. Zbl0137.36203MR346957
  15. [15] SCHUR, I., (1923), Über eine Klasse von Mittelbildungen mit Anwendungen die Determinanten, Theorie Sitzungsber. Berlin. Math. Gesellschaft, Vol. 22, pp.9-20. JFM49.0054.01
  16. [16] SIBSON, R. (1979), Studies in the robustness of multidimensional scaling: perturbational analysis of classical scaling, J. Royal Stat. Soc. B, Vol. 41, pp. 217-229. Zbl0413.62046MR547248

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