Date of Award
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.
Weiskircher, Alvena, "A STUDY OF VECTOR AND MATRIX NORMS" (1973). Theses, Dissertations & Honors Papers. 433.