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Mapping geometry for 2 by 2 matrices - Editorial Review

Dan Kalman

Dan Kalman's Mapping Geometry module allows linear algebra students to visualize linear transformations of the form Ax = y, where A is a 2 by 2 matrix. The module is based on Mathwright Microworld technology, an HTML document format that allows embedding of portals used to display "story pages." To use it, users must first download and install MathwrightWeb ActiveX Control (which is available for free) for Internet Explorer. There is also a stand-alone (Windows only) version available on the site. Mapping Geometry consists of two web pages that are very similar in form. They differ only in that the first page contains two boxes of Cartesian planes, one for drawing domain points and second for drawing image points, whereas the second page displays both domain and image points inside one box. Each page allows the user to define a matrix A and then to select one of four possible modes by clicking on buttons: Click Points, Circle, Polygon, and Drag Points. Editing the entries of A can be done easily by using the keyboard and clicking on the "Change A" button. Each mode allows a different representation of domain vectors so that the resulting image vectors can be studied. This tool will help students visualize linear transformations in R2, being particularly helpful in illustrating the geometric interpretation of eigenvectors.

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Dan Kalman, "Mapping geometry for 2 by 2 matrices - Editorial Review," Loci (June 2004)