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T : V --> V is linear operator on a finite - dimensional vector space V. The cha

ID: 1946803 • Letter: T

Question

T : V --> V is linear operator on a finite - dimensional vector space V. The characteristic polynomial of T is the characteristic polynomial of a matrix that represent T realavtive to some basis for V.



HOW THIS STAEMENT IS TRUE?

Explanation / Answer

T : V --> V is linear operator on a finite - dimensional vector space V. The characteristic polynomial of T is the characteristic polynomial of a matrix that represent T relative to some basis for V. Vector space V having linear operator T from vector space V to itself, T having characteristic polynomial which is also the polynomial of matrix representing some basis for V. So the statement is true.