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# Browsing Auburn Theses and Dissertations by Author "Tam, Tin-Yau"

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### Asymptotic Results in Noncompact Semisimple Lie Groups

Thompson, Mary Clair (2013-04-22)

This dissertation is a collection of results on analysis on real noncompact semisimple Lie groups. Specifically, we examine the convergence patterns of sequences arising from the special group decompositions that exist ...

### 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. ...

### Convexity of Generalized Numerical Ranges Associated with SU(n) and SO(n)

Tadesse, Dawit Gezahegn (2010-05-20)

We give a new proof of a result of Tam on the convexity of the generalized numerical
range associated with the classical Lie groups SO(n). We also provide a connection between
the result and the convexity of the classical ...

### Differential geometry on matrix groups

Gan, Luyining (2020-03-20)

In this dissertation, we study the differential geometry of the matrix groups. In literatures, many authors proposed to compute matrix means using the geodesic distance defined by an invariant Riemannian metrics on the ...

### 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, ...

### 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 ...

### Gradient Flows, Convexity, and Adjoint Orbits

Liu, Xuhua (2012-06-19)

This dissertation studies some matrix results and gives their Generalizations in the context of semisimple Lie groups. The adjoint orbit is the primary object in our study.
The dissertation consists of four chapters. ...

### The Lattice Gas Model and Lattice Boltzmann Model on Hexagonal Grids

Jin, Kang (2005-08-15)

We present an overview of the FHP model and the Lattice BGK model. Details regarding boundary conditions and initial conditions are discussed throught implementations on driven cavity flow, Poiseuille flow, and flow past ...

### Minimum Power Consumption for Rate Monotonic Tasks

Huang, Chiao (2008-12-15)

Embedded computer systems are widely used in modern life and their use is expanding. One of the typical constraints in embedded systems, particularly in standalone devices, is their low power capacity. One way to expand ...

### On the Conjugacy Theorems of Cartan and Borel Subalgebras

Thompson, Mary Clair (2010-04-09)

We study the conjugacy theorems of Cartan subalgebras and Borel
subalgebras of general Lie algebras. We present a history of the problem, along with two proofs of the theorems which stay completely within the realm of ...

### Products of positive definite symplectic matrices

Granario, Daryl Quebrar (2020-07-15)

We show that every symplectic matrix is a product of five positive definite symplectic
matrices and five is the best in the sense that there are symplectic matrices which are not product
of less.

### 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 ...