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(Solved): Taking into consideration that \epsi may contain any number of elements and may even be an infinite ...



Taking into consideration that \epsi may contain any number of elements and may even be an infinite set. Suppose \epsi is a subset of L(V) and every element of \epsi is diagonalizable. Prove that there exists a basis of V with respect to which every element of \epsi has a diagonal matrix if and only if every pair of elements of \epsi commutes.


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