Agenda, Semester Week 9

General Vector Spaces

This week will introduce the concept of vector spaces. Objects in a vector space are as such not different from the vectors we worked with last week, but this week we treat them in a more generalized manner. For instance, a vector space might consist of other mathematical objects than vectors, such as matrices or polynomials. In particular we will study how linear (in)dependence can be understood in this more general setting, and we will cover concepts such as subspaces, (ordered) bases, coordinate vectors as well as change-of-basis matrices for vector spaces.

Key Terms

Vector spaces. Linear (in)dependence in a vector space. (Ordered) basis of a vector space and corresponding coordinate vectors. Change-of-basis matrices. Subspaces.

Preparation and Syllabus

This week will cover Sections 10.1 through 10.4 from Chapter 10 in [the textbook].

Note that Section 10.5 is not a part of the syllabus.

Exercises

Exercises for Long Day. A SymPy test in Möbius for Python module 2 will take place 15:30-17:00 on Long Day.

Exercises for Short Day.