# MATH 4570 - Advanced Linear Algebra

Class information:

Homework:

 HW 1 Do the problems from here. The solutions are here. HW 2 Do the problems from here. The solutions are here.   Also do HW 7 #1--8 from my MATH 2550 website.   The solutions are on the 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. HW 3 Do the problems from here. The solutions are here.   Also do HW 10 # 1--2 from my MATH 2550 website. The solutions are on the 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 do HW 10 # 3--8 from my MATH 2550 website. The solutions are on the 2550 website.Note: In the Math 2550 HW, P_n means P_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. HW 6 Do the problems from here. The solutions are here.

My Notes:

• Part 1 - Vector spaces and subspaces
• Part 2 - Spanning sets, linear independence, bases, and dimension
• Part 3 - Linear transformations

• Part 4 - The matrix of a linear transformation
Extra: Here is a picture that give a summary of part 4.

• Review - A review of determinants

• Part 5 - Eigenvalues, eigenvectors, and diagonalization
Extra: Motivation: pic 1, pic 2.   This goes at page 75 in the notes.
Extra: In class we redid the theorem on pgs 77-78.   Here are the pics: pic 1, pic 2, pic 3, pic 4

• Part 6 - Inner product spaces
• Part 7 - A few final comments about diagonalization on inner product spaces

​Test solutions:

Online Resources: