Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

6: Orthogonality and Least Squares

( \newcommand{\kernel}{\mathrm{null}\,}\)

  • 6.1: The Dot Product
  • 6.2: Orthogonal Complements and the Matrix Tranpose
    This section introduces the notion of an orthogonal complement, the set of vectors each of which is orthogonal to a prescribed subspace. We'll also find a way to describe dot products using matrix products, which allows us to study orthogonality using many of the tools for understanding linear systems that we developed earlier.
  • 6.3: Orthogonal bases and projections
  • 6.4: Finding Orthogonal Bases
  • 6.5: Orthogonal Least Squares
    n this section, we'll explore how the techniques developed in this chapter enable us to find the line that best approximates the data. More specifically, we'll see how the search for a line passing through the data points leads to an inconsistent system Ax=b. Since we are unable to find a solution x, we instead seek the vector x where Ax is as close as possible to b. Orthogonal projection give us just the right tool for doing this.


This page titled 6: Orthogonality and Least Squares is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by David Austin via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?