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Numerical analysis of a correlation matrix. (English) Zbl 0874.62065

Summary: We present some new results on a definite positive symmetric matrix: We prove that each term of such a matrix belongs to an interval which depends on the other ones and we give a relation between entries, the interval in which each entry belongs to, and the corresponding entry of the inverse matrix. So these properties give a new interpretation in the case of correlation matrices: correlation coefficients are bounded given the other ones, and partial correlation coefficients are defined from the intervals. We finally give numerical examples computed by programs available from the author.

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62J05 Linear regression; mixed models
65C99 Probabilistic methods, stochastic differential equations
15A23 Factorization of matrices
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References:

[1] Ciarlet P. G., Introduction to Numerical Linear Algebra and Optimisation (1989)
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[5] DOI: 10.1002/0471725153 · doi:10.1002/0471725153
[6] DOI: 10.2307/1267351 · Zbl 0202.17205 · doi:10.2307/1267351
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