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Week 10 Short Day: Diagonalization by Similarity Transformation

If a square matrix is similar to a diagonal matrix, it is said to be diagonalizable via a similarity transformation. This is closely connected to the eigenvalue problem. Today we will investigate the conditions that make diagonalization possible and how it can be carried out.

Today’s Key Concepts

Similar matrices. Diagonalization by similarity transformation.

Prepartion and Syllabus

Today we continue with subjects from eNote 13 Eigenvalues and Eigenvectors about the eigenproblem. New material is eNote 14 Similarity and Diagonalization, which can be considered “the matrix version” of the eigenproblem.

Maple Ressources

We can do with already known Maple commands.

Today’s Maple demo is Diagonalization

Activity Program

  • 13.00 – 14.00: $\,$No live lecture today (lecturer is absent). See the pre-recorded lecture on this link, or show up as usual in Auditorium 42 at 13:00 where the recording will be shown.
  • 14.00 – 16.00: $\,$Group exercises in the study areas (b. 302, bottom floor)
  • 16.00 – 17.00: $\,$Weekly Test.

Group Exercises

  1. Linear Map with Given Eigenvectors
  2. Eigenvalue Problems in 3D Space
  3. Maple Exercise in Reverse
  4. Diagonalization by Similarity Transformation
  5. Similar Matrices
  6. Complex Diagonalization Using Maple

Weekly Test

For all Weekly Tests, the following applies:

  • The test is an on-location test, meaning it can only be accessed in the study area.
  • No electronic aids are allowed (except for your own notes on e.g. a tablet).
  • The test can be accessed in the the Möbius quiz system via a link on DTU Learn in the module for 01006 (in the top menu click “Möbius”).
  • The TA will provide a code for Möbius test access.
  • You must be in full-screen mode so the test fills the whole screen.
  • Your solutions to the test questions must be typed into Möbius without in-between calculations or steps. The result is automatically evaluated by Möbius.
  • To ensure a smooth experience use the Firefox or Chrome browser, and disable any add-blocker.
  • Use a DTU network.
  • You may discuss the test questions with fellow students in your study group, but you have your own version of the test with scrambled numbers that you yourself must solve and enter into Möbius.
  • During the final hour on Fridays you have one attempt. Passing this attempt will grant you 1 bonus point. From Friday at 18:00 until Wednesday at 18:00 the test is reopened for repeated attempts. Passing during this phase will grant you ½ bonus point.