MA 305 Lecture 19 Transparencies

Thursday, April 6, 2000

Slide 1

Review of topics.
Orthogonality.
(Audio part 1, 2:00)

Slide 2

Theorem of Pythagorus.
Motivation for orthogonality: Find nearest vector that has a solution.
(Audio part 1, 11:00 and 41:30)

Slide 3

Example: Least Squares and Hook's law.
(Audio part 1, 23:30)

Slide 4

Scalar product of two vectors.
(Euclidean) norm of vector.
Angle between two vectors.
Orthogonality of vectors.
(Audio part 1, 38:30 and 42:30; and part 2, 15:00)

Slide 5

Orthogonal projection in R².
(Audio part 2, 3:00)

Slide 6

Dual concept with respect to orthogonal projection: creating a space of all vectors orthogonal to line. (Orthogonal complement).
Orthogonality of subspaces.
(Audio part 2, 11:00, 16:00, 18:30, and 24:00)

Slide 7

Orthogonal complement of a space.
(Audio part 2, 17:00 and 19:00)

Slide 8

Example of orthogonal complement.
(Audio part 2, 21:30 and 25:00)