Week Program, Semester Week 10

Linear Maps

This week we will be dealing with linear maps. Linear maps are special functions between vector spaces. A linear map gives rise to two special subspaces: the kernel and the image space. The rank-nullity theorem ties together the dimensions of these spaces. By using ordered bases a linear map can be described using a matrix, called the mapping matrix. Such matrices can be used to compute the kernel and the image space of a linear map.

Key Terms

Linear maps, kernel and image space of a linear map, mapping matrix, change-of-basis matrix, the rank-nullity theorem.

Preparation and Syllabus

This week covers [10 - Linear maps between vector spaces].

Exercises

Exercises for Long Day.

Exercises for Short Day.