Matrix Norms

Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

E. E. Underwood


E. E. Underwood


In many situations it is very useful to have a single nonnegative real number to be, in some sense, the measure of the size of a vector or a matrix. As a matter of fact we do a similiar thing with scalars, we let jÀj represent the familiar absolute value or modulus of À. Fora vector x e: C , one way n of assigning magnitude is the usual definition of length, Il I 1/2 2 1/2 xl= = {jxij } , which is called the euclidean norm of x. In this case, length gives an overall estimate of the size of the elements of x. If llxll is large, at least one of the elements in x is large, and vise versa. There are many ways of defining norms for vectors and matrices. We will examine some of these in this paper.