Geodesic
Inverting covariance matrices
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 163-177

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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.
Keywords: multi-way classification, cross, hierarchical, balanced, unbalanced, covariance matrix, inverting 
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Stępniak, Czesław. Inverting covariance matrices. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 163-177. http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a3/