Applied algebra for informatics MSc (2017 fall)

Exercises

Problem set 1 and the solutions
Problem set 2 and the solutions
Problem set 3 and the solutions

Lecture notes:

Vector spaces, linear maps and matrices
Eigenvalues, eigenvectors, diagonalization
Jordan normal form
Euclidean spaces and its transformations
Singular value decomposition

Practice classes

October 5, Thursday, 10.15, T606
October 13, Friday, 12.15, T606

Midterm exam

October 19, Thursday, 8.15, E202
Make-up test: november 2, Thursday, 10.15, R504
List concepts, theorems and computational methods that you need to know for the test.
The midterm test and its solution

Exam

It is a written exam, most of it is problem solving but there will also be a question about definitions and theorems (as in the midterm test) and you are also expected to know the proof of some of the theorems (marked by a cirled P in the lecture notes):
Fisher's inequality
Eigenvalues are roots of the minimal polynomial
Characteristic and minimal polynomials of Jordan blocks
Eigenvalues of unitary and self-adjoint matrices
Rank and definiteness of ATA
Best approximate solution

Further reading

You can find a more detailed discussion of basic linear algebra and some of the more advanced topics in this notes of James S. Cook . He also gives a list of further linear algebra books with comments on pages 3 and 4.