MA 305 Lecture 7 Transparencies

Thursday, February 1st, 2001

Slide 1

(0:06) Efficient computation of the Fibonacci numbers. (Aside) Associativity of binary operators.

Lecture 7, slide 1

Slide 2

(0:11) (Aside continued) Is division an associative binary operator?

Lecture 7, slide 2

Slide 3

(0:14) How to compute powers efficiently: successive squaring (aka binary exponetiation). How many integer operations?

Lecture 7, slide 3

Slide 4

(0:23) How many operations do we use to multiply two matrices?

Lecture 7, slide 4

Slide 5

(0:35) (aside) The Golden Ratio. Transposition of matrices.

Lecture 7, slide 5

Slide 6

(0:41) Example of transposition, and some of the properties of transposition. Matrix symmetry.

Lecture 7, slide 6

Slide 7

(0:44) Example of a symmetric matrix. Identity matrices.

Lecture 7, slide 7

Slide 8

(0:57) Diagonal matrices, the matrix inverse.

Lecture 7, slide 8

Slide 9

(1:05) Notation for the matrix inverse. Uniqueness of the inverse, and using it to solve linear systems.

Lecture 7, slide 9

Slide 10

(1:09) Matrices without inverses?

Lecture 7, slide 10

Slide 11

(1:12) Computing the inverse of the Fibonacci matrix.

Lecture 7, slide 11