# MATH 4570 - Advanced Linear Algebra

Class information:

Test solutions:

Study guides:

Past Lecture Notes:

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) andM_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 9 # 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 9 - # 3--8  and  HW 7 (Part 1) - # 9(b,c), 10(b,c), 11Note: 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.

Schedule and lecture notes:

 Week Monday Wednesday 1 8/22 lecture notes 8/24 lecture notes 2 8/29 lecture notes 8/31 lecture notes 3 9/5 HOLIDAY 9/7 lecture notes 4 9/12 lecture notes 9/14 lecture notes 5 9/19 lecture notes 9/21 6 9/26 lecture notes 9/28 lecture notes 7 10/3 lecture notes 10/5 TEST 1 8 10/10 lecture notes 10/12 lecture notes 9 10/17 lecture notes 10/19 lecture notes 10 10/24 lecture notes 10/26 lecture notes 11 10/31 lecture notes 11/2 lecture notes 12 11/7 lecture notes 11/9 lecture notes 13 11/14 lecture notes 11/16 TEST 2 11/21 HOLIDAY 11/23 HOLIDAY 14 11/28 lecture notes 11/30 lecture notes 15 12/5 lecture notes 12/7 lecture notes Finals week 12/14 Final exam time 12pm - 2pm

Online Resources: