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Kunze Linear Algebra
· Problem 3.2.8
Linear Transformations
Mathematics — Methods · nilpotent-operator
Problem
Let
V
V
V
be a vector space over the field
F
F
F
and
T
T
T
a linear operator on
V
V
V
. If
T
2
=
0
T^2 = 0
T
2
=
0
, what can you say about the relation of the range of
T
T
T
to the null space of
T
T
T
? Give an example of a linear operator
T
T
T
on
R
2
R^2
R
2
such that
T
2
=
0
T^2 = 0
T
2
=
0
but
T
≠
0
T \neq 0
T
=
0
.
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