Matrix operators in 3-space are harder to represent and visualize than they are in 2-space, so we present only a few simple samples. More complicated matrix operators can be found by generalizing the operators below or combining them with other linear operators.
To find the matrix operators which project onto the other coordinate planes, change the positions of the 1's on the diagonal of the above matrix.
Projection onto the x-y-plane
To find the matrix operators which project onto the other coordinate axes, change the location of the 1 on the diagonal of the above matrix.
Projection onto the z-axis
To find the matrix operators which reflect in the other coordinate planes, change the location of the -1 on the diagonal of the above matrix.
Reflection in the x-y-plane
To find the matrix operators which reflect in the other coordinate axes, change the locations of the -1's on the diagonal of the above matrix.
Reflection in the z-axis
To find the matrix operators which rotate about the other coordinate axes, swap rows and corresponding columns of this matrix to put the 1 elsewhere on the diagonal.
Rotation about the z-axis


A Catalogue of Simple Matrix Operators

Introduction Projections in 2-space Reflections in 2-space Scale changes in 2-space
Shears in 2-space Rotations in 2-space A sampler of 3-space matrix operators