Part 5: Summary
- How is a rotation in the
plane represented by a matrix?
- How is a rotation around
one of the axes in 3-space represented by a matrix?
- State two properties of
multiplication of 2-dimensional rotation matrices -- one algebraic and
- From your explorations in Part 3, what did you learn about when products of 3-dimensional rotation matrices commute?
The remaining questions
are based on Part 4. Answer them as best you can from the
evidence gained from 2-dimensional and special 3-dimensional rotation matrices.
(The properties observed in Part 4 hold for all rotation matrices.)
- What is the determinant
of a rotation matrix?
- How can you write down
the inverse of a rotation matrix by inspection?
- What is the geometric significance
of the inverse of a rotation matrix?
- What are the special properties
of the rows of a rotation matrix? of the columns?
modules at math.duke.edu