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On Wielandt’s inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix. (English) Zbl 0742.62015

Authors’ summary: A relatively obscure eigenvalue inequality due to H. Wielandt [in “Topics in the analytic theory of matrices.” Univ. Wisconsin Press, Madison (1967)] is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.

MSC:

62E20 Asymptotic distribution theory in statistics
62H25 Factor analysis and principal components; correspondence analysis
15A18 Eigenvalues, singular values, and eigenvectors
15B52 Random matrices (algebraic aspects)
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