Vector and Matrix Norms

Abstract

In multidimensional calculus, vector and matrix norms quantify notions of topology and convergence [2, 4, 5, 6, 8, 12]. Because norms are also devices for deriving explicit bounds, theoretical developments in numerical analysis rely heavily on norms. They are particularly useful in establishing convergence and in estimating rates of convergence of iterative methods for solving linear and nonlinear equations. Norms also arise in almost every other branch of theoretical numerical analysis. Functional analysis, which deals with infinite-dimensional vector spaces, uses norms on functions.