Browsing by Author "Holmes, Randall"

Now showing items 1-12 of 12

A Brief Exploration of the Sorgenfrey Line and the Lexicographic Order

Greiwe, Regina (2006-05-15)

The author will compare properties of the usual topology on the real line with the properties of the Sorgenfrey Line. After that she will look at properties of the Lexiographic Order on the reals cross [0,1]. The main ...

Coefficient Space Properties and a Schur Algebra Generalization

Turner, David (2005-12-15)

Let K be an infinite field and Gamma = GL_(n)(K). If we linearly extend the natural action of Gamma on the set E of n-dimensional column vectors over K to the group algebra KGamma, then E becomes a KGamma-module. We then ...

A Comparison of Two Proofs of Yamamoto's Theorem Relating Eigenvalue Moduli and Singular Values of a Matrix

Pell, Melinda (2006-12-15)

We examine two proofs of Yamamoto’s theorem regarding the asymptotic relationship between singular values and eigenvalue moduli of a matrix. The first proof is by T. Yamamoto in 1967 and makes use of compound matrices. ...

Extensions of Monotonicity Results to Semisimple Lie Groups

Sarver, Zachary (2016-05-05)

We extend a monotonicity result of Wang and Gong on the product of powers of positive definite matrices. This result concerns the eigenvalues of such products which written as vectors have a log majorization relationship. ...

Generalization of Ky Fan-Amir-Moez-Horn-Mirsky's result on the eigenvalues and real singular values of a matrix

Yan, Wen (2005-12-15)

Ky Fan's result states that the real part of the eigenvalues of an n by n com- plex matrix A is majorized by the eigenvalues of the Hermitian part of A. The converse was established by Amir-Moez and Horn, and Mirsky, ...

Generalizations of Various Results in Quantum Computation Theory to Mixed-Dimensional Quantum Systems

Gay, Randall (2021-04-05)

The majority of the research in quantum computation theory is based on quantum mechanical systems consisting of quantum subsystems that are all of the same dimension. Following and expanding on the research conducted by ...

Geometric means inequalities and their extensions to Lie groups

Ahsani, Sima (2018-12-05)

This dissertation has two main parts. 1. After reviewing the Riemannian structure of the space of n n positive de nite matrices, Pn, and the geometric mean in terms of geodesic, t-geometric mean, we present some ...

On O-Basis Groups and Generalizations

Ervin, Jason (2007-08-15)

A class of finite groups which we call o-basis groups is generalized and explored. One reason for interest in these groups lies with the concept's origins. The notion of o-basis group arose from the study of the existence, ...

Population Ecology of Northern Bobwhites

Folk, Travis (2006-05-15)

The longleaf pine (Pinus palustris) ecosystem is an ecologically significant region of North America, yet its geographic extent has been greatly reduced by several factors including anthropogenic fire suppression. There ...

Progress on the Marcus-de Oliveira Determinantal Conjecture

Homadi, Khadejah (2017-04-12)

We discuss the well known conjecture of Marcus and de Oliveira of the determinant of the sum of normal matrices. We present the motivation of this conjecture, along with detailed history of its origin. Then we compile ...

Structure Theory and a Generalization of the Isomorphism Theorems

Bertl, Alan (2013-07-10)

A general format in which the mathematical structure of topological spaces, algebraic structures, and graphs can be expressed is described. A generalization of the fundamental homomorphism theorem and the isomorphism ...

Toeplitz Matrices are Unitarily Similar to Symmetric Matrices

Liu, Jianzhen (2017-07-25)

We prove that Toeplitz matrices are unitarily similar to complex symmetric matrices. Moreover, two $n\times n$ unitary matrices that uniformly turn all $n\times n$ Toeplitz matrices via similarity to complex symmetric ...