Work Description

READMEFIRST FILE Overview: The Singular Value Decomposition (SVD) has become widely used by the scientific and technical communities. The list of applications of the SVD not only grows, but accelerates; 3,000,000 Google pages now mention SVD, with particularly central positioning in the areas of Principal Component Analysis, data compression, latent semantic analysis, linguistics, numerical analysis, econometrics, search engines and recommendation engines. The object of our project is to provide researchers and students with a tool to allow them to develop an intuitive understanding of singular vectors and singular values. Matrices having size 2x2 matrices with real entries map circles to ellipses. In particular, a unit circle centered at the origin is mapped to an ellipse centered at the origin, and it is well known that in this case the points on the ellipse that are farthest from the origin are the same points that give rise to the first singular vectors. We provide an interactive GUI in which the users can key in the entries for a 2x2 matrix of their choice and then self-explore to visually locate the singular vector, and then readout its numeric values. By doing this for several matrices, users can develop their intuition for relating the entries of the matrix to the resulting shape of the ellipse, and thereby being able to make a reasonable guess at the singular vectors and singular value. File Inventory: The four files included are : 1) the ReadMeFirst file, 2) the short introductory paper entitled The Self-Discovery Module (GUI) for Singular Vectors: The �Greatest Stretch� Method for 2x2 Matrices, 3) the downloadable interactive GUI itself, entitled Self-Discovery of Singular Vectors and Values, written in JavaScript and therefore usable free of charge on almost all computers immediately after downloading without further need of other software, and 4) a pdf copy the JavaScript program. Development Period: The introductory paper and the GUI were produced over a period of four months by a member of the Department of Mathematics and Statistics at the University of Michigan � Dearborn and a student in Computer Science. Use: Files 1), 2) and 4) are immediately accessible, while the GUI must be downloaded to the user�s computer.