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2002 SNSB Admission
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1
Part of
2002 SNSB Admission
Problems
(1)
Condition for the endomorphisms of finite vec. spaces to be nilpotent
Source: Admission to SNSB, 2002
10/4/2019
Let
u
,
v
u,v
u
,
v
be two endomorphisms of a finite vectorial space that verify the relation
u
v
−
v
u
=
u
.
uv-vu=u.
uv
−
vu
=
u
.
Calculate
u
k
v
−
v
u
k
u^kv-vu^k
u
k
v
−
v
u
k
and show that u is nilpotent.
Field theory
vector spaces
linear algebra