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A good test on how well do you know matrix theory

Source: IMC 2022 Day 1 Problem 2

August 5, 2022
linear algebramatrixIMC 2022

Problem Statement

For a positive integer nn determine all n×nn\times n real matrices AA which have only real eigenvalues and such that there exists an integer k≥nk\geq n with A+Ak=ATA + A^k = A^T.
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