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The user selects the coefficients of a 2 by 2 matrix and drags a red arrow about $$R^2$$.  The application shows the image of the red arrow under the matrix as a blue arrow.

The user selects from several matrices that represent basic transformations of the plane.  The application shows the images of the standard basis under the transformation, and the user can sel

The user produces a new basis $$\{u,v\}$$ for $$R^2$$ by moving points on a plane, and can then move a point around $$R^2$$ by altering the $$u$$ and $$v$$ coordinates of the point.  It takes

This application takes a random 4 by 4 matrix and applies the QR algorithm to it.  Users see the resulting matrix at each step, and also can see (if they choose) the values of the eigenvalues

This application allows users to manipulate two vectors $$v_1$$ and $$v_2$$.  Also shown are the orthogonal projection of $$v_2$$ onto $$v_1$$ and the new Gram-Schmidt vectors $$u_1=v_1$$ and

This application steps users through the Gram-Schmidt process applied to three vectors in $$\mathbf{R}^3$$.  The user has a large number of choices for the initial vectors.  Users can el

This application interprets a 3 by 3 system graphically in two ways: as the intersection among three planes, and as the expression of a vector as a linear combination of three vectors.  Users

This application allows the student to work through several examples of a 3 by 3 system and to see the geometrical result of individual row operations.  The system can be presented either as a

This MOOC, offered by Coursera, was developed by Philip Klein of Brown University.

This is a very intriguing text.