For each linear operator T on V, find the minimal polynomial of T. (a) V = R2 and T(a, b) = (a + b, a −b) (b) V = P2(R) and T(g(x)) = g’(x) + 2g(x) (c) V = P2(R) and T(f(x)) = −xf”(x) + f’(x) + 2f(x) (d) V = Mn×n(R) and T(A) = At. Hint: Note that T2 = I.
For each linear operator T on V, find the minimal polynomial of T. (a) V = R2 and T(a, b) = (a + b, a −b) (b) V = P2(R) and T(g(x)) = g’(x) + 2g(x) (c) V = P2(R) and T(f(x)) = −xf”(x) + f’(x) + 2f(x) (d) V = Mn×n(R) and T(A) = At. Hint: Note that T2 = I.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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For each linear operator T on V, find the minimal polynomial of T.
(a) V = R2 and T(a, b) = (a + b, a −b)
(b) V = P2(R) and T(g(x)) = g’(x) + 2g(x)
(c) V = P2(R) and T(f(x)) = −xf”(x) + f’(x) + 2f(x)
(d) V = Mn×n(R) and T(A) = At. Hint: Note that T2 = I.
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