Principal component analysis : some majorisation, perturbation and nonnegative matrix theory
Statistique et analyse des données, Tome 13 (1988) no. 1, pp. 8-14.
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     url = {http://www.numdam.org/item/SAD_1988__13_1_8_0/}
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Critchley, Frank. Principal component analysis : some majorisation, perturbation and nonnegative matrix theory. Statistique et analyse des données, Tome 13 (1988) no. 1, pp. 8-14. http://www.numdam.org/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 | Zbl

[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 | Zbl

[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 | Zbl

[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

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

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

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

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

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

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

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

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

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

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

[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 | Zbl