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Back to Polynomials of Maps and Matrices

Exercise 1

Avg difficulty 3.0

What are the possible minimal polynomials if a matrix has the given characteristic polynomial?

  • (a)  (x−3)4(x-3)^{4}     (b)  (x+1)3(x−4)(x+1)^{3}(x-4)     (c)  (x−2)2(x−5)2(x-2)^{2}(x-5)^{2}     (d)  (x+3)2(x−1)(x−2)2(x+3)^{2}(x-1)(x-2)^{2}

What is the degree of each possibility?

Hefferon, Linear Algebra, Similarity, Polynomials of Maps and Matrices, Exercise 1

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.