Matrix representation for transformation

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The discussion centers on the representation of transformations using matrices, specifically addressing the concept of similar matrices. It clarifies that two matrices, A and B, being non-similar indicates that there is no matrix P that satisfies the equation P^{-1}AP = B. The original poster shares their attempt at a solution on their blog, asserting that they see no errors in their reasoning. The conversation emphasizes the importance of understanding matrix similarity in the context of transformations. Overall, the thread highlights key concepts in linear algebra related to matrix representation and transformation.
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I see nothing wrong with it. I was at first taken aback that you could do that with non-similar matrices but of course, saying that two matrices, A and B, are not similar only means there does not exist a single matrix, P, such that P^{-1}AP= B. Your Q is not the inverse of P.
 

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