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Rank Cancellation Rule

In: Matrix Tricks for Linear Statistical Models

Author

Listed:
  • 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)

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.

Suggested Citation

  • Simo Puntanen & George P. H. Styan & Jarkko Isotalo, 2011. "Rank Cancellation Rule," Springer Books, in: Matrix Tricks for Linear Statistical Models, chapter 0, pages 145-150, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-10473-2_7
    DOI: 10.1007/978-3-642-10473-2_7
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