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This is a video of a handwritten explanation of eigenvalues and eigenvectors. Nothing fancy, but it is effective.

This is a nicely-designed applet that is effective at displaying the effect of a $$2 \times 2$$ matrix transformation.

For a fixed matrix, users can drag one or two vectors to locate eigenvectors geometrically.

For a fixed matrix, users can drag one or two vectors to locate eigenvectors geometrically.

There is nothing too fancy here. Users can define their own $$2 \times 2$$ matrix either numerically or by dragging vectors that correspond to the columns of the matrix.

This applet is very effective at displaying the Gerschgorin circles associated with the eigenvalues of a $$4 \times 4$$ matrix.

Very nice applet that does a good job showing how composition of linear transformations works.

This applet displays the Gerschgorin circles assocaited with $$3 \times 3$$ to $$8 \times 8$$ matrices. Pre-defined or random matrices acan be selcted. User-defined matrices are not possible.

Simple applet that illustrates eigenvectors/eigenvalues of $$2 \times 2$$ matrices.

Simple but effective applet. Does a good job of visually demonstrating eigenvectors and how a basis of eigenvectors leadds to matrix diagonalization.