Year
2010
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
First Advisor
Dr. Damon Hay
Second Advisor
Dr. Richard F. Patterson
Third Advisor
Dr. Daniel L. Dreibelbis
Department Chair
Dr. Scott Hochwald
College Dean
Dr. Barbara A. Hetrick
Abstract
This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is applied to image compression by using reduced rank matrix approximations to represent greyscale images. MATLAB results for approximations of JPEG and .bmp images are presented. The results indicate that images can be represented with reasonable resolution using low rank matrix SVD approximations.
Suggested Citation
Kwizera, Petero, "Matrix Singular Value Decomposition" (2010). UNF Graduate Theses and Dissertations. 381.
https://digitalcommons.unf.edu/etd/381