Math 8530, Spring 2017
# Math 8530, Spring 2017

"We share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury." --Irving Kaplansky, writing of himself and Paul Halmos

Class
Syllabus

### Lecture Notes

Section 1:
Vector spaces. (12 pages, last updated Jan 23, 2013. slides)

Section 2:
Duality. (6 pages. Updated Jan 30, 2013.)

Section 3:
Linear mappings. (14 pages. Updated Feb 14,
2011. slides)

Section 4:
Matrices. (9 pages. Updated Feb 19, 2015)

Section 5:
Determinant and trace. (17 pages. Updated February 19, 2015)

Section 6:
Spectral theory. (22 pages. Updated June 20, 2017)

Section 7:
Euclidean structure. (23 pages. Updated April 2, 2013)

Section 8:
Self-adjoint mappings. (17 pages. Updated April 16, 2013)

Section 9:
Positive definite mappings. (19 pages. Updated May 3, 2013)

### Homework

Homework 1: pdf |
tex. Due
Thursday, January 19.

Homework 2: pdf |
tex. Due
Thursday, January 26.

Homework 3: pdf |
tex. Due
Tuesday, February 7.

Homework 4: pdf |
tex. Due
Tuesday, February 14.

Homework 5: pdf |
tex. Due
Tuesday, February 21.

Homework 6: pdf |
tex. Due
Thursday, March 2.

Homework 7: pdf |
tex. Due Thursday,
March 9.

Homework 8: pdf |
tex. Due Thursday,
March 16.

Homework 9: pdf |
tex. Due Thursday,
March 30.

Homework 10: pdf |
tex. Due Thursday,
April 6.

Homework 11: pdf |
tex. Due Tuesday,
April 18.

Homework 12: pdf |
tex. Due Thursday,
April 27.