Unformatted text preview: Z n . (g) Find a quadratic polynomial f ( t ) (with coeﬃcients depending on n ) such that f ( Z n ) = 0. (h) Use (g) to calculate the inverse of Z n , expressed as a linear combination of Z n and I n . (This generalizes Problem Set 7, Problem 3.) 2. Let T : V → V be a linear operator, where V is ﬁnite dimensional. Suppose that W 1 ,...,W k are Tinvariant subspaces of V such that T W i is diagonalizable for each i . Prove that if W 1 + ··· + W k = V , then T is diagonalizable. 3. Section 5.4, Exercises 13 and 20....
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 Fall '08
 GUREVITCH
 Linear Algebra, Algebra, Characteristic polynomial, Zn, Jn, Haiman Problem Set

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