[Univ of Cambridge] [Dept of Engineering]

EIGEN

This program is based on a procedure discussed in first year mathematics lectures on Matrices and Eigenvalues. It is designed to help first-year undergraduates obtain a feel for some of the basic concepts in this subject.

The program carries out an analysis of the linear transformation y = Ax, where A is a general 2 x 2 matrix, and demonstrates graphically the component matrices which result from this analysis. The graphical technique which is used shows the effect of the matrix on a grid of uniform squares.

The matrix A is rewritten as the product of a symmetric matrix and an orthogonal one and these are demonstrated to the student in terms of a rigid body rotation followed by a symmetric 'straining'.

The program finally calculates the eigenvalues and eigenvectors associated with the symmetric part of the matrix A and shows how lines parallel to the eigenvectors retain their directions during the straining process.


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Updated on 12th December, 1997
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