Ivan Shishkin, Rye (1878)

Problems/Linear algebraUnreviewed

Nilpotency cannot tell ABAB from BABA

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This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
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These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Let A,B∈Mn(R)A,B \in \mathcal{M}_n(\R) and P∈R[X]P\in \R[X]. Show that P ⁣(eAB)P\!\left(e^{{AB}} \right) is nilpotent if and only if P ⁣(eBA)P\!\left(e^{{BA}} \right) is nilpotent.

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