6: Orthogonality and Least Squares
- Page ID
- 82501
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- 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.
- 6.5: 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.