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CIIM 2013 Problem 5

Source:

June 9, 2016
CIIM 2013CIIMundergraduate

Problem Statement

Let A,BA,B be n×nn\times n matrices with complex entries. Show that there exists a matrix TT and an invertible matrix SS such that B=S(A+T)S−1 −T  ⟺  tr⁡(A)=tr⁡(B) B=S(A+T)S^{-1}\ -T \iff \operatorname{tr}(A) = \operatorname{tr}(B)
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