Displaying similar documents to “Representation theory and statistics”

Indecomposable (1,3)-groups and a matrix problem

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2013)

Czechoslovak Mathematical Journal

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Almost completely decomposable groups with a critical typeset of type ( 1 , 3 ) and a p -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p k , either no indecomposables if k ≤ 2 ; only six near isomorphism types of indecomposables if k = 3 ; and indecomposables of arbitrary large rank if k ≥ 4 .

The determination of factors in linear models of factor analysis

Petr Kratochvíl (1990)

Aplikace matematiky

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The author shows that a decomposition of a covariance matrix ∑ = 𝐀𝐀 ' implies the corresponding model, i.e. the existence of factors f j such that ∑ a i j f j is true. The result is applied to the general linear model of factor analysis. A procedure for computing the factor score is proposed.

Block diagonalization

Jaromír J. Koliha (2001)

Mathematica Bohemica

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We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.