5: Vector Space Rⁿ
( \newcommand{\kernel}{\mathrm{null}\,}\)
- 5.1: Subspaces and Spanning
- In this chapter we investigate Rn in full generality, and introduce some of the most important concepts and methods in linear algebra.
- 5.2: Independence and Dimension
- Some spanning sets are better than others. Our interest here is in spanning sets where each vector in U has exactly one representation as a linear combination of these vectors.
- 5.6: Best Approximation and Least Squares
- Often an exact solution to a problem in applied mathematics is difficult to obtain. However, it is usually just as useful to find arbitrarily close approximations to a solution. In particular, finding “linear approximations” is a potent technique in applied mathematics. One basic case is the situation where a system of linear equations has no solution, and it is desirable to find a “best approximation” to a solution to the system.