We have already learned about transformation matrices and linear transformations. What do you think the modifier “orthogonal” implies when we say, “orthogonal transformation”? Do you suspect an orthogonal transformation will satisfy all the same properties that general transformations satisfy? Justify our reasoning.
In section 4.2, we saw how linear transformations can transform a two-dimensional object in the plane. Consider the vertex matrix T = [■(0&1&1&0@0&1&-1&0)] in application 1 page 185. How can we extend this into 3 dimensional objects in space? Add a vector, or vectors to T and describe the object for which you have created vertices (i.e., a cube, a pyramid, etc.)