I am struggling to understand similarity of two matrices. I got that similar matrices represent the same linear map for different bases, but I have a question about it which I can't answer. Suppose I have two different linear maps T1: R2 --> R2 and T2: R2 --> R2. B1, B2, C - bases of R2. M1 is standard matrix for T1 with respect to B1 and standard matrix for T2 with respect to B2 simultaneously and M2 is standard matrix for T1 with respect to C and isn't standard matrix of T2 at all. As you see, if we consider transformation T1, then M1 and M2 are similar, but they can't be similar if we consider T2. Is this situation possible or I miss something? If possible, isn't it ambiguity in definition of similarity? Thanks for help.
2026-03-25 12:48:43.1774442923
Ambiguity in similarity definition
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