Vector and Matrix Norms
This chapter begins the study of numerical linear algebra. The length, or norm, of a vector is defined, and the 2-, 1-, and infinity vector norms are defined. There are inequalities that bound each norm in terms of the others. The chapter develops properties of the 2-norm, since it is most frequently used in applications. In particular, the Cauchy-Schwarz inequality and the Pythagorean theorem are satisfied by the 2-norm. The 2-norm is orthogonally invariant and thus is very important in computer graphics. If a set of k vectors in n-dimensional space are orthogonal, they form a basis for a k-dimensional subspace. Multiplication by an orthogonal matrix effects a change of coordinates. Spherical coordinates ...
Get Numerical Linear Algebra with Applications now with O’Reilly online learning.
O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.