Date of Award


Degree Type

Honors Paper




A vector or matrix can be associated with a single nonnegative scalar . Basically this is the concept of a vector or matrix norm. While the study of these norms may be classified as numerical analysis , a limited background in linear algebra , matrix theory , and advanced calculus is sufficient to pursue the study of norms.

In this paper many of the properties and theorems concerning norms have been proven . It is thought that the most important results deal with the use of vector and matrix norms in testing for convergence of sequences and series of matrices and vectors.

The geometry of norms is beneficial in clarifying many properties. In fact several proofs make use of geometrical definitions of norms .

Most of the theorems and proofs in the paper are known results; however, it was for the purpose of collecting, organizing and providing details necessary for understanding these proofs that the paper was written.

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.