Suppose V is a complex vector space and T 2 L.V / is invertible.Let p denote the

Chapter 8, Problem 10

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Suppose V is a complex vector space and T 2 L.V / is invertible.Let p denote the characteristic polynomial of T and let q denote thecharacteristic polynomial of T 1. Prove thatq.z/ D 1p.0/ zdim V p1zfor all nonzero z 2 C.

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