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The determination of factors in linear models of factor analysis

Petr Kratochvíl — 1990

Aplikace matematiky

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.

On convergence of homogeneous Markov chains

Petr Kratochvíl — 1983

Aplikace matematiky

Let p t be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences p t + 2 - p t + 1 < p t + 1 - p t . In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains.

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