16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.3.9

Elementary Canonical Forms

Mathematics — Linear Algebra · trace-characteristic-polynomial

Problem

Let AA be an n×nn \times n matrix with characteristic polynomial f=(x−c1)d1⋯(x−ck)dk.f = (x - c_1)^{d_1} \cdots (x - c_k)^{d_k}. Show that c1d1+⋯+ckdk=trace(A).c_1 d_1 + \cdots + c_k d_k = \text{trace}(A).

Related theory

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