Math 8530, Spring 2015
# Math 8530, Spring 2015

"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)

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

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

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

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

Section 6:
Spectral theory. (24 pages. Updated March 13, 2013)

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
Tuesday, January 20.

Homework 2: pdf |
tex. Due
Tuesday, January 27.

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

Homework 4: pdf |
tex. Due
Tuesday, February 10.

Homework 5: pdf |
tex. Due
Tuesday, February 17.

Homework 6: pdf |
tex. Due
Tuesday, February 24.

Homework 7: pdf |
tex. Due Friday,
March 6.

Homework 8: pdf |
tex. Due Friday,
March 13.

Homework 9: pdf |
tex. Due Friday,
March 27.

Homework 10: pdf |
tex. Due Friday,
April 3.

Homework 11: pdf |
tex. Due Friday,
April 10.

Homework 12: pdf |
tex. Due Monday,
April 20. [Old version: pdf | tex]

Homework 13: pdf |
tex. Due Friday,
April 21.