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The animation illustrates the matrix-vector product, $$Ax$$, computed as linear combinations of the columns of $$A$$.  The weights in the linear combination are the components of $$x$$.

A nice example of a sequence of proof steps to show that the sum of the eigenvalues is equal to the trace. Illustration of some good practices in proofs.

Visulization of eigenvector by tracking $$x$$ vs. $$Ax$$. A sweep operation makes it easy to line up the vectors; the user can stop the sweep.

Visualization of eigenvectors by rotating and lining up an input vector $$x$$ and output vector $$Ax$$. Several matrices are used to explain topics.

Well-organized list of online resources with links. A collection of sites and materials for linear algebra. Extensive list that includes videos, applets, applications, etc.

Requires down loading the free CDF player from Wolfram (https://www.wolfram.com/cdf-player/).  A wide variety of applets that vary in form.

Find the sum and dot product of two vectors in two dimensions. The pair of vectors can be dragged to different position with the parallelogram following along.

View the action of a linear transformation on a two dimensional shape. Built-in shapes are the unit circle, unit square, and a star. The 2 by 2 matrix can is entered in a grid.

A collection that includes linear algebra and phyisics; 7 in linear algebra. Each carefully illustrates the concepts involved. Easy to use.

These modules are designed for students to explore, experiment, conjecture, discuss, and extend their understandings from the concrete to the abstract.