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.