Rank Cancellation Rule

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 6 in Matrix Tricks for Linear Statistical Models, 2011, pp 145-150 from Springer

Abstract: Abstract If $$ a \in \mathbb{R}$$ and $$ y \in \mathbb{R}$$ have property $$ ay \neq 0,$$ then trivially 6.1 $$lay = may \Longrightarrow la = ma,$$ that is, we can cancel y from (6.1) (as well as a). For matrices, the corresponding cancellation does not work. However, there is a very handy trick, the rank cancellation rule, which allows cancellations for matrices in the style of (6.1). It seems, according to our experience, that this simple rule has not received so much appreciation in statistical literature as it earns.

Date: 2011
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DOI: 10.1007/978-3-642-10473-2_7

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