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Week 8 Short Day: Mapping Matrices and Change of Basis

We will today continue our work with linear maps and their mapping matrices and we will study typical examples of how to determine their kernels and images. An important point is that when the the basis is changed in the domain or codomain, the mapping matrix for the linear transformation changes as well.

Today’s Key Concepts

Linear transformation (or mapping). Mapping matrix. Kernel and range. Linear equations and the structural theorem. Basis change for a mapping matrix.

Preparation and Syllabus

Today’s content is covers topics from eNote 12 Linear Transformations from Section 12.8.

Maple Syllabus

Today we can do with already known Maple-commands. We just have to use them properly, as today’s Maple demo will showcase: ChangeOfBasisAndMapping.

Activity Program

  • 13.00 – 14.00: $\,$Lecture (aud. 42, b. 303A) (link to streaming)
  • 14.00 – 16.00: $\,$Group exercises in the study areas (b. 302, bottom floor)
  • 16.00 – 17.00: $\,$Weekly Test.

Group Exercises

  1. Typical Questions about Linear Maps
  2. Conclusions about the Reduced Mapping Matrix
  3. New Mapping Matrix from Change of Basis
  4. Linear Maps in Abstract Vector Spaces
  5. Linear Mapping and Change of Basis. Maple
  6. Extra Training Exercise on Linear Mappings