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DISTRIBUTIONS IN R WITH ROTATIONAL SYMMETRIES 1
Author(s) -
Watson G. S.
Publication year - 1983
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1983.tb00392.x
Subject(s) - eigenvalues and eigenvectors , linear subspace , unit vector , combinatorics , mathematics , invariant (physics) , rotational invariance , distribution (mathematics) , multivariate random variable , unit (ring theory) , mathematical analysis , physics , pure mathematics , random variable , mathematical physics , quantum mechanics , statistics , algorithm , mathematics education
Summary Let X ∈ R be a random vector with a distribution which is invariant under rotations within the subspaces V j (dim V j . = q j ) whose direct sum is R. The large sample distributions of the eigenvalues and vectors of M n = n ‐1 Σ n l x i x i are studied. In particular it is shown that several eigenvalue results of Anderson & Stephens (1972) for uniformly distributed unit vectors hold more generally.