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Self-Discovery Module (GUI) for Singular Vectors: The"Greatest Stretch" Method for 2x2 Matrices

Creator:

James, David A. and Lokam, Nikhil

Description:

The object of this project is to provide researchers and students with a tool to allow them to develop an intuitive understanding of singular vectors and singular values. 2x2 matrices A with real entries map circles to ellipses; in particular, unit circles centered at the origin to ellipses centered at the origin. It is known that the points on the ellipse farthest from the origin correspond to the singular vectors of A. Users can use the GUI to enter matrices of their choice and explore to visually self-determine the singular vectors/values.

Keyword:

SVD, Singular Value Decomposition, Singular Vector, Singular Value, and Matrix

Discipline:

Science and Engineering