Question: Exercise 4.4: [5 points] Let V be a vector space and let p E C(V) be a projector. Prove that V = ker(p) Dim(p). Show

Exercise 4.4: [5 points] Let V be a vector space and let p E C(V) be a projector. Prove that V = ker(p) Dim(p). Show also that any projector can be represented in an appropriate basis by the matrix Er O Ap = 0 where Er is the rxr unit matrix with r = dim im(p), and the zeros stand for (n-r) x (n-r) matrices with zero entries (n = dim V )

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