Similar Matrices

MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Ben Harris

A teaching assistant works through a problem on similar matrices.

License: Creative Commons BY-NC-SA

[tomctutor]

*Caution* (b) is True in this specific case, not in general!
You can have matrices that share same characteristic equation (hence same eigenvalues) but are not necessarily similar. 
An example might be where multiplicities of eigenvalues are involved so the eigenvectors are incomplete set in one but complete in another matrix.

[ashadds]

a is wrong this guy mixed up things, B = M-1AM, not MAM-1, reference dr strangs previous lecture

[jbuttercup]

Super helpful for a project I'm working on! I was just wondering though.. at 5:30 it says that similarity preserves eigenvalues AND eigenvectors. I thought it was only eigenvalues?

[justpaulo]

In (c), initially, I actually thought you were using the result from (a) and building a polynomial, but you were actually checking the evectors using J-λI

[Robocat]

Apparently this instructor did not take Gilbert Strang's lectures. The method used In (c) does not work for the example in the last lecture where two matrices have the same number of eigenvectors but they are not similar.

[Haider_Waseem_]

Thank you so much, Sir. Appreciated. #Pakistan