Easy Column Space Tricks

Simo Puntanen (), George P. H. Styan () and Jarkko Isotalo ()
Additional contact information
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 1 in Matrix Tricks for Linear Statistical Models, 2011, pp 57-70 from Springer

Abstract: Abstract The column space of an n × m matrix A, 1.1 $$\mathcal{C} (A_{n \times m}) = \{{\bf y} \in \mathbb{R}^n: \text{there exists}\ {\bf x} \in \mathbb{R}^m \text{such that}\ {\bf y} = {\bf Ax}\}, $$ and, correspondingly, the null space of A, 1.2 $$\mathcal{N} (A_{n \times m}) = \{{\bf x} \in \mathbb{R}^m: {\bf Ax} = 0\}, $$ are in every-day use throughout this book. In this chapter we take a good look at some of their properties, most of them rather elementary. Our experience is that decent steps in linear models are slow to take unless a reasonable set of column space tricks is in the immediate access. Some of the results that we go through are already likely to be in the reader’s toolbox. However, there cannot be harm in repeating these helpful rules and going through their proofs.

Keywords: Parametric Function; Full Column Rank; Column Space; Independent Column; Black Widow (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-10473-2_2

Ordering information: This item can be ordered from
http://www.springer.com/9783642104732

DOI: 10.1007/978-3-642-10473-2_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().