Math 104.01 (Linear Algebra)

Spring 1997

Plan for Week 13

The word this week is ORTHOGONAL -- from the Greek roots orthos (right) and gonia (angle). The corresponding word of Latin origin (from the words for "plumb line") is perpendicular -- which is a synonym for orthogonal. This is not a new idea in your study of mathematics, but it is an idea that has played no significant role thus far in this course. We have seen some bases of mutually perpendicular bases, such as the standard basic vectors in Rⁿ, and we have seen some important bases that are usually not perpendicular: bases of eigenvectors. We have seen some good algebraic reasons for preferring bases of "special directions" -- for example, in decoupling dynamical systems. But there are also good reasons -- mostly geometric -- for preferring mutually orthogonal bases. For example, these bases help us analyze the projections needed for computer graphics. This emphasis on the geometric aspects of linear algebra will continue into the next (and last full) week of the course.

To see the syllabus for Week 13 in a separate window, click here.

1. Your next homework papers will be turned in on Monday, April 19. Those papers should include solutions to all problems in the assignment below. The assignment dates are start dates.
2. In general, no solution will be given full credit unless you have written an explanation of why you know it is correct. (Exceptions to this rule are the exercises whose numbers appear in parentheses.)

Assignments

• Monday, Apr. 12, Sec. 6.1 / #(1), (2), (6), (7), 11, (14), (15), 19, 20, 23, (26), 27, 28, 30, 31
• Wednesday, Apr. 14, Sec. 6.2 / #(1), (4), (6), 9, (11), 13, 14, (15), 17, 23, 24, 29, 33, 34
• Friday, Apr. 16, Sec. 6.3 / #1, 4, 5, 9, 11, 14, 17, 19, 21, 22, 25

Last modified: March 16, 1999