Displaying similar documents to “Mathematical foundations of multivariate path analysis”

Inversion of 3 × 3 partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters

Karel Hron (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a 3 × 3 partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for 2 × 2 partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas...

Decomposing matrices with Jerzy K. Baksalary

Jarkko Isotalo, Simo Puntanen, George P.H. Styan (2008)

Discussiones Mathematicae Probability and Statistics

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In this paper we comment on some papers written by Jerzy K. Baksalary. In particular, we draw attention to the development process of some specific research ideas and papers now that some time, more than 15 years, has gone after their publication.

Factorizations for q-Pascal matrices of two variables

Thomas Ernst (2015)

Special Matrices

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In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]

Inverting covariance matrices

Czesław Stępniak (2006)

Discussiones Mathematicae Probability and Statistics

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Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.

Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods

Mika Mattila, Pentti Haukkanen (2016)

Special Matrices

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Let T = {z1, z2, . . . , zn} be a finite multiset of real numbers, where z1 ≤ z2 ≤ · · · ≤ zn. The purpose of this article is to study the different properties of MIN and MAX matrices of the set T with min(zi , zj) and max(zi , zj) as their ij entries, respectively.We are going to do this by interpreting these matrices as so-called meet and join matrices and by applying some known results for meet and join matrices. Once the theorems are found with the aid of advanced methods, we also...