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