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Let g(t) be the auxiliary polynomial associated with a homogeneous linear differential

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence ISBN: 9780130084514 53

Solution for problem 11 Chapter 7.3

Linear Algebra | 4th Edition

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Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

Linear Algebra | 4th Edition

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Problem 11

Let g(t) be the auxiliary polynomial associated with a homogeneous linear differential equation with constant coefficients (as defined in Section 2.7), and let V denote the solution space of this differential equation. Prove the following results. (a) V is a D-invariant subspace, where D is the differentiation operator on C. (b) The minimal polynomial of Dv (the restriction of D to V) is g(t). (c) If the degree of g(t) is n, then the characteristic polynomial of Dv is(-l)n g(t). Hint: Use Theorem 2.32 (p. 135) for (b) and (c).

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Chapter 7.3, Problem 11 is Solved
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Textbook: Linear Algebra
Edition: 4
Author: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
ISBN: 9780130084514

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Let g(t) be the auxiliary polynomial associated with a homogeneous linear differential