MAT247H1 Lecture Notes - Lecture 1: Dihedral Group, Linear Map, Group Homomorphism
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Problem set 8(questions 1 15), due thursday april 2; questions 3b), 4, 8b), 10a) and 15b) will be marked. Problem set 9, questions 16 29; not to be handed in: let t be a linear operator on a nite-dimensional complex vector space. 4 t r for some positive integer r. prove that t is diagonalizable if and only if t 3 = 4 t . (hint: What can you say about the minimal polynomial of t ?: let v = p2(r). Let = { t + 1, t 1, t2 1}, and let = { f1, f2, f3 } be the dual basis for. Express f as a linear combination of the basis vectors f1, f2 and f3: let v = p2(r) = { p(t) = a + b t + c t2 | a, b, c r}. Let v be the dual space of v .
