Matrix Plots in Support of Visualization of Matrix Characteristics

• Activity Number: 343
• Type: Contributed
• Date/Time: Tuesday, July 31, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Ferry Butar Butar* and Wathurawa A. Bandulasiri and Melinda M. Holt and Cecil Hallum+
• Companies: Sam Houston State University and Sam Houston State University and Sam Houston State University and Sam Houston State University
• Keywords: matrices ; visualization ; plots ; pseudoinverse

Abstract

By its structure, a matrix can easily be visualized graphically. This can be useful (or, at least, interesting) in providing a means to visualize some of its associated characteristics. Numerous matrices result from a convergent sequence of matrices; for example, the pseudoinverse is known to result from a convergent sequence (similar to the sequence used in ridge regression). In such situations, one can "watch" a matrix "go to its pseudoinverse" (i.e., graphically). The singular value decomposition of a symmetric matrix is expressible as a convergent sequence of matrices; again, here one can visualize a matrix converge to its singular value decomposition (or the square root) of a given matrix. This paper investigates a number of such situations whereby visualization are quite insightful. The pros and cons of such an approach will be reported along with accompanying examples.