Definition of projection and related facts

Reference no: EM132520353

Question 1: For the definition of projection and related facts, see pages 76-77. Let V be a vector space and T: V → V be a linear transformation. Prove that T = T² if and only if T is a projection on W₁ = {y T(y) = y} along N (T).

Question 2: Let β be an ordered basis for a finite-dimensional vector space V, and let T: V → V be linear. Prove that, for any nonnegative integer k, [T^k]_β = ([T]_β)^k.

Reference no: EM132520353

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