The Matrix $$\dot{\rm M}$$

Simo Puntanen (), George P. H. Styan () and Jarkko Isotalo ()
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Simo Puntanen: University of Tampere, School of Information Sciences
George P. H. Styan: McGill University, Department of Mathematics & Statistics
Jarkko Isotalo: University of Tampere, School of Information Sciences

Chapter Chapter 15 in Matrix Tricks for Linear Statistical Models, 2011, pp 317-342 from Springer

Abstract: Abstract It is well known that if V is a symmetric positive definite n × n matrix, and (X : Z) is a partitioned orthogonal n × n matrix, then $$({\bf X}^{\prime}{\bf V}^{-1}{\bf X})^{-1} = {\bf X}^{\prime}{\bf V}{\bf X} - {\bf X}^{\prime}{\bf V}{\bf Z}({\bf Z}^{\prime}{\bf V}{\bf Z})^{-1}{\bf Z}^{\prime}{\bf V}{\bf X}.$$ .

Keywords: Related Reference; Full Column Rank; Column Space; Prove Proposition; Cancellation Rule (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-10473-2_16

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