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

 

 

 

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


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

lecture notes
        +
proof of theorem
from class

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

     +

proof of 
theorem from
class

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: