The discussion revolves around the definitions of similar matrices and their diagonalization in linear algebra, specifically addressing the placement of the matrices C and C^-1 in the equations. The original poster questions the consistency of these definitions and whether they are correctly represented in their lecture notes.
Participants are exploring the definitions and questioning the assumptions behind them. Some participants seek clarification on whether additional context or definitions were omitted from the original poster's explanation. There is an acknowledgment of the potential for misunderstanding due to reliance on lecture notes rather than a standard textbook.
The discussion highlights that the definitions being referenced come from lecture notes rather than a published textbook, which may contribute to the confusion. The original poster is also considering the implications of these definitions for calculating powers of matrices.
That couldn't possibly have been the definition your book gave. What did you omit?cookiesyum said:My linear algebra textbook defines...
similar matrices: A = C^-1BC
Hurkyl said:That couldn't possibly have been the definition your book gave. What did you omit?
Nothing else, really? Nothing likecookiesyum said:Nope, that's it! He has us using his own lecture notes, instead of a published textbook. This is why I thought it could potentially be an error.