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Exercise 6

Avg difficulty 3.0

Find the minimal polynomial of matrices of this form

(λ00…01λ0001λ⋱λ000…1λ)\begin{pmatrix}\lambda&0&0&\ldots&&0\\ 1&\lambda&0&&&0\\ 0&1&\lambda\\ &&&\ddots\\ &&&&\lambda&0\\ 0&0&\ldots&&1&\lambda\end{pmatrix}

where the scalar λ\lambda is fixed (i.e., is not a variable).

Hefferon, Linear Algebra, Similarity, Polynomials of Maps and Matrices, Exercise 6

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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.