Principal component analysis : some majorisation, perturbation and nonnegative matrix theory
Critchley, Frank
Statistique et analyse des données, Tome 13 (1988), p. 8-14 / Harvested from Numdam
Publié le : 1988-01-01
@article{SAD_1988__13_1_8_0,
     author = {Critchley, Frank},
     title = {Principal component analysis : some majorisation, perturbation and nonnegative matrix theory},
     journal = {Statistique et analyse des donn\'ees},
     volume = {13},
     year = {1988},
     pages = {8-14},
     mrnumber = {984842},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SAD_1988__13_1_8_0}
}
Critchley, Frank. Principal component analysis : some majorisation, perturbation and nonnegative matrix theory. Statistique et analyse des données, Tome 13 (1988) pp. 8-14. http://gdmltest.u-ga.fr/item/SAD_1988__13_1_8_0/

[1] Berman, A. and Plemmons, R.J., (1979), Non-negative matrices in the mathematical sciences, London: Academic Press. | MR 544666 | Zbl 0484.15016

[2] Critchley, F., (1983), The Euclideau structure of a dendrogram, Warwick Statistics Research Report No. 48.

[3] Critchley, F., (1985), Influence in principal components analysis, Biometrika, Vol. 72, pp. 627-636. | MR 817577 | Zbl 0608.62068

[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. | MR 34519 | Zbl 0041.00602

[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. | JFM 40.0202.02

[6] Hoph, E., (1963), An inequality for positive integral linear operators, J. Math. and Mech., Vol. 12, pp. 683-692. | MR 165325 | Zbl 0115.32501

[7] Horn, A., (1954), Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math., Vol. 76, pp. 620-630. | MR 63336 | Zbl 0055.24601

[8] Kendall, M.G. (1975), Multivariate analysis, London: Griffin. | Zbl 0551.62032

[9] Marshall, A.W. and Olkin, I., (1979), Inequalities: theory of majorization and its applications, London: Academic Press. | MR 552278 | Zbl 0437.26007

[10] Mirsky, L., (1958), Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc, Vol. 33, pp. 11-21. | MR 91931 | Zbl 0101.25303

[11] Morrison, D.F., (1976), Multivariate statistical methods, London: McGraw-Hill. | MR 408108 | Zbl 0355.62049

[12] Ostrowski, A.M. (1963), On positive matrices, Math. Annalen. Vol. 150, pp. 276-284. | MR 148680 | Zbl 0115.24803

[13] Perron, O. (1907), Zur Theorie der Über Matrizen, Math. Ann., Vol. 64, pp. 248-263. | JFM 38.0202.01 | MR 1511438

[14] Rao, C.R., (1973), Linear statistical inference and its applications, London: John Wiley. | MR 346957 | Zbl 0137.36203

[15] Schur, I., (1923), Über eine Klasse von Mittelbildungen mit Anwendungen die Determinanten, Theorie Sitzungsber. Berlin. Math. Gesellschaft, Vol. 22, pp.9-20. | JFM 49.0054.01

[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. | MR 547248 | Zbl 0413.62046