A 2-inverse for a matrix A is any matrix G satisfying GAG=G. This book adresses the special, but heretofore ignored, role of 2-inverses in statistics. The relationship among various kinds of generalized inverses and their construction in terms of 2-inverses are explored. The applications discussed include the role of 2-inverses in: canonically representing second-degree polynomials x'Ax+b'x+c, obtaining vectors � which satisfy K'�=0 and minimize y'y-X�(squared), and relating the hypotheses tested by various analytical approaches in generalized linear models. For each topic, the simplification of both the concepts and the notation which results from a 2-inverse approach is stressed and illustrated with examples.

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Articles li�s � 2 - Inverses and Their Statistical Application

2 - Inverses and Their Statistical Application

Getson, Albert J./ Hsuan, Francis C.

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