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The {2}-inverse with applications in statistics

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
70
Identifiers
DOI: 10.1016/0024-3795(85)90055-2
Disciplines
  • Mathematics

Abstract

Abstract An inverse G of a given matrix A which satisfies the property GAG = G is known as a {2}-inverse. This paper presents a three-phase inversion procedure for which the {2}-inverse is a special case. We present the geometry of {2}-inverses and show that, starting from {2}-inverses, various types of generalized inverses can be derived. Two examples of the occurrence of {2}-inverses in statistics are given: one concerning the constrained least-squares estimator, the other concerning a necessary and sufficient condition for a quadratic form of singular multivariate normal variates to follow a chi-square distribution.

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