Question: Explain why the following statement is nonsense. Two linear operators F and G on a vector space V are said to be similar if there

Explain why the following statement is nonsense.

Two linear operators F and G on a vector space V are said to be similar if there exists an invertible linear operator T on V such that G = T 1 F T. If F is similar to a diagonal matrix, then any similar matrix G is also similar to a diagonal matrix.

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