MA 305 Lecture 25 Transparencies

Tuesday, April 25, 2000

Slide 1

Orthogonal projection.
Example of orthogonal projection.
(Audio part 1, 3:30, 12:30, and 22:00)

Lecture 25, slide 1

Slide 2

Example of orthogonal projection continued. (Least squares problem.)
(Audio part 1, 8:30)

Lecture 25, slide 2

Slide 3

Orthogonal set.
Review of multilinearity of inner product.
(Audio part 1, 18:30)

Lecture 25, slide 3

Slide 4

Orthogonal basis.
Projection onto orthonormal basis.
(Audio part 1, 19:30, 23:00, 26:00, 33:00 and 37:00)

Lecture 25, slide 4

Slide 5

Orthogonal projection of one vector onto another.
Examples of inner products.
(Audio part 1, 24:00 and 26:30)

Lecture 25, slide 5

Slide 6

Projection onto orthogonal basis.
Example of orthogonal projection revisited.
(Audio part 1, 34:00)

Lecture 25, slide 6

Slide 7

Projection onto orthogonal basis continued.
Gram-Schmidt orthogonalization.
(Audio part 1, 37:30; and part 2, 4:00 and 23:00)

Lecture 25, slide 7

Slide 8

Gram-Schmidt orthogonalization.
(Audio part 2, 7:00, 17:00, and 22:00)

Lecture 25, slide 8

Slide 9

Example of Gram-Schmidt orthogonalization.
(Audio part 2, 18:00 and 25:00)

Lecture 25, slide 9