Linear Algebra

Cliff uses J with his Linear Algebra classes. For example, in the fall of 2003 he used nine J laboratories with his linear algebra class. The labs were:

1. Curve Fitting by Solving Linear Systems
   Introduction to J, simple system solving, high degree polynomial fit and fitting values and derivatives.
2. Traffic Flow
   An application of Gauss-Jordan to giving the general solution to a network flow problem.
3. Geometric Transformations of the Plane
   Experiments with transformations in the plane: rotations, scaling, translations and using them for animations.
4. Transition Matrices
   Interpreting and experimenting with Markov matrices
5. Properties of Determinants
   Exercises in discovering properties of determinants and applications to volumes of k-dimensional parallelipipeds in n-dimensional space.
6. Geometric Transformations in Three Dimensions
   Experiments with transformations in 3-space and animations.
7. Frame's Method, Eigenvalues and Spotted Owls
   Implementation of a technique for finding the characteristic polynomial and eigenvalues and application to a model of the Spotted owl population.
8. Power Method, Inverse Power Method and Rayleigh Quotient Iteration
   Introduction to other techniques for finding eignevalues and application to artful images of basins of attraction.
9. Projection and Least Squares Fitting
   Introduction to such computations and graphing solutins. Application to wine sale data.

These laboratories are currently written in PCTeX format. Faculty interested in browsing copies are welcome to request copies: email: reiterc@lafayette.edu. Exchanges welcome. See also At Last for other ideas for linear algebra laboratories.

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