If you represent vectors r = xi + yj in 2-space by column matrices, then matrix operators are transformations given by a formula of the form

for some 2 x 2 matrix , called the standard matrix of the transformation. (The columns of the standard matrix are the transforms of the vectors i and j.)

This catalogue lists many of the more common matrix operators in 2-space. Each entry gives the standard matrix of the operator and a bimodal diagram showing a typical vector before and after the operation is applied.

On the last page, there is a sampler of operators on 3-space, of the form

These entries have the same format as those for 2-space: the standard matrix and a before-and-after diagram for a typical vector.