MATH 4570 - Advanced Linear Algebra

Class information:

Syllabus

Test solutions:

Study guides:

Past Lecture Notes:

Notes from Fall 2020
Notes from Fall 2021

My notes: These are the notes that I'm using to teach the class.
The specific notes for this semester's class are in the calendar
below with a link to each day's notes.
Feel free to use these if you want to look ahead.

Topic 0 - Review row reduction - see Topic 3 notes from Math 2550
Topic 1 - Vector spaces
Topic 2 - Spanning sets, linear independence, bases, dimension
Topic 3 - Linear transformations
Topic 4 - The matrix of a linear transformation
Review - Determinants
Topic 5 - Eigenvalues, eigenvectors, diagonalization

Homework:

HW 0	HW 0 is optional. It is for you to review row reduction from Math 2550 if you haven't done it for a while. If you do the homework below and look at the solutions it is a good review. Do HW 3 from my MATH 2550 website. Note: Do as many of the above so you understand the three situations: (a) no solutions (b) exactly one solution (c) infinitely many solutions Infinitely many can have one or more variables that parameterize the solutions.
HW 1	Do the problems from here. The solutions are here.
HW 2	Do the problems from here. The solutions are here. Do HW 7 (part 1 and part 2) from my MATH 2550 website. Note: In the Math 2550 HW, P_n means P_n(R) and M_2,2 means M_2,2(R) where R is the set of real numbers. Note: If you want more practice finding dimensions of vector spaces, you can try to find the dimensions of the subspaces from HW 1 - #2 above.
HW 3	Do the problems from here. The solutions are here. Also do HW 10 # 1--2 from my MATH 2550 website. Note: In the Math 2550 HW, P_n means P_n(R) and M_m,n means M_m,n(R).
HW 4	Do the problems from here. The solutions are here. Also from my MATH 2550 website do these problems: HW 10 - # 3--8 and HW 7 (Part 1) - # 9(b,c), 10(b,c), 11 Note: In the Math 2550 HW, P_n means P_n(R) and M_m,n means M_m,n(R).
Review of Determinants	For review, do HW 5 from my MATH 2550 website. The solutions are on the 2550 website.
HW 5	Do the problems from here. The solutions are here. Here is another way to do #3a (reverse direction).
HW 6	Do the problems from here. The solutions are here.