A pseudo-euclidean operator norm of linear operators in finite dimensional spaces.

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Date
October, 2019
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Abstract
This thesis introduces a certain operator norm on linear operators in finite di mensional spaces which we will call pseudo-Euclidean p-norm. We show the computation of the operator norm of linear operators in one-dimensional, two dimensional and three-dimensional spaces. The study obtained in the thesis is with respect to computation of the operator norm on the linear operator of finite dimensional spaces and comparing to those of the standard operator norms. This thesis basically gives detailed definitions and some few historical remarks about a Hilbert space as well as detailed review of the mathematics involved. Detailed proofs of theorems, propositions, lemmas and corollaries leading up to the com putation of the main work are provided. Finally, the main work, computing the pseudo-Euclidean operator norm of linear operators in finite dimensional spaces is carried out and compared with the usual matrix p-norm in some instances
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology, in partial fulfillment of the requirements for the award of master of philosophy degree in pure mathematics,
Keywords
Operator norm, pseudo-euclidean
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