MathDB
property of traces

Source: SEEMOUS 2012 P3

June 9, 2021
matrixlinear algebra

Problem Statement

a) Prove that if kk is an even positive integer and AA is a real symmetric n×nn\times n matrix such that tr⁡(Ak)k+1=tr⁡(Ak+1)k\operatorname{tr}(A^k)^{k+1}=\operatorname{tr}(A^{k+1})^k, then An=tr⁡(A)An−1.A^n=\operatorname{tr}(A)A^{n-1}. b) Does the assertion from a) also hold for odd positive integers kk?
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