Rank of the Partitioned Matrix and the Matrix Product

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 5 in Matrix Tricks for Linear Statistical Models, 2011, pp 121-144 from Springer

Abstract: Abstract There are numerous situations in the world of linear models and multivariate analysis when we need to find some appropriate expressions for the rank of the matrix product AB, or of the partitioned matrix (A : B), for conformable matrices A and B. Our favourite expressions are represented in the following theorem.

Keywords: Model Matrix; Matrix Product; Nonzero Eigenvalue; Full Column Rank; Column Space (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-10473-2_6

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