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Condition for the endomorphisms of finite vec. spaces to be nilpotent

Source: Admission to SNSB, 2002

October 4, 2019
Field theoryvector spaceslinear algebra

Problem Statement

Let u,v u,v be two endomorphisms of a finite vectorial space that verify the relation uv−vu=u. uv-vu=u. Calculate ukv−vuk u^kv-vu^k and show that u is nilpotent.
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