Question: Let V be a finite-dimensional vector space, and suppose that T : V V is a linear function. (a) Show that there exist bases and

Let V be a finite-dimensional vector space, and suppose that T : V V is a linear function. (a) Show that there exist bases and for V such that [T] is a diagonal matrix. (b) Suppose that S : V V is another linear function. Show that there are bases , , , for V such that [T] = [S]_,

if and only if dim(ker(T)) = dim(ker(S)).

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