Show that every linear map from a 1-dimensional vector space to itself ismultiplication

Chapter 3, Problem 7

(choose chapter or problem)

Show that every linear map from a 1-dimensional vector space to itself ismultiplication by some scalar. More precisely, prove that if dim V D 1and T 2 L.V; V /, then there exists 2 F such that T v D v for allv 2 V.

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