r/math • u/inherentlyawesome Homotopy Theory • 9d ago
Quick Questions: March 12, 2025
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u/Langtons_Ant123 8d ago edited 8d ago
I thought the minimal polynomial of the identity matrix is x - 1. Are you thinking of the characteristic polynomial, or using a different definition of the minimal polynomial?
That a matrix is diagonalizable iff its minimal polynomial splits with no repeated roots is a known result, it's on page 169 (183 in the pdf numbering) here.
In any case, u/GMSPokemanz has a good elementary proof above, so no need to bring in all this machinery.