A Numerical Approach to the Approximate and the Exact Minimum Rank of a Covariance Matrix
- 1 June 1991
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 56 (2) , 309-315
- https://doi.org/10.1007/bf02294464
Abstract
A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.Keywords
This publication has 7 references indexed in Scilit:
- The Rank of Reduced Dispersion MatricesPsychometrika, 1987
- Minimum Rank and Minimum Trace of Covariance MatricesPsychometrika, 1982
- Weighted Minimum Trace Factor AnalysisPsychometrika, 1982
- Rank-Reducibility of a Symmetric Matrix and Sampling Theory of Minimum Trace Factor AnalysisPsychometrika, 1982
- Computational Aspects of the Greatest Lower Bound to the Reliability and Constrained Minimum Trace Factor AnalysisPsychometrika, 1981
- Inequalities Among Lower Bounds to Reliability: With Applications to Test Construction and Factor AnalysisPsychometrika, 1980
- The approximation of one matrix by another of lower rankPsychometrika, 1936