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Math 115B: General Course Outline

Catalog Description

115B. Linear Algebra. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition. P/NP or letter grading.

Textbook

S. Friedberg, et al, Linear Algebra, 4th Ed., Prentice-Hall.

Schedule of Lectures

Lecture Section Topics

1

.

Review of Math 115A, Chapters I and II

2

2.6

Dual Spaces (This section looks short but the concepts are new and thus will take two lectures to do well)

3

2.6

Dual Spaces

4

.

Review Sections 5.1 and 5.2 from 115A

5

5.4

Invariant Subspaces and the Cayley Hamilton Theorem

6

5.4

Invariant Subspaces and the Cayley Hamilton Theorem

7

5.4

Invariant Subspaces and the Cayley Hamilton Theorem

8

.

Review Sections 6.1 - 6.4 including more detail than was done in 115A

9

.

Review Sections 6.1 - 6.4 including more detail than was done in 115A

10

6.5

Unitary and Orthogonal Operators and their matrices

11

6.5

Unitary and Orthogonal Operators and their matrices

12

6.5

Unitary and Orthogonal Operators and their matrices

13

6.6

Orthogonal Projections and the Spectral Theorem

14

6.6

Orthogonal Projections and the Spectral Theorem

15

6.6

Orthogonal Projections and the Spectral Theorem

16

.

EXAM

17

6.11

The Geometry of Orthogonal Operators

18

6.11

The Geometry of Orthogonal Operators

19

6.11

The Geometry of Orthogonal Operators

20

7.1

Jordan Canonical Form I (This is a long and intricate presentation that takes time; do examples along the way!)

21

7.1

Jordan canonical Form I

22

7.1

Jordan canonical Form I

23

7.3

The Minimal Polynomial (It might actually be better to do this section right after the Cayley Hamilton Theorem)

24

7.3

The Minimal Polynomial

25-29

.

At the discretion of the teacher.