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Kunze Linear Algebra
· Problem 5.4.8
Determinants
Mathematics — Methods · determinant-commutator-operator
Problem
Let
V
V
V
be the vector space of
n
×
n
n \times n
n
×
n
matrices over the field
F
F
F
. Let
B
B
B
be a fixed element of
V
V
V
and let
T
B
T_B
T
B
be the linear operator on
V
V
V
defined by
T
B
(
A
)
=
A
B
−
B
A
T_B(A) = AB - BA
T
B
(
A
)
=
A
B
−
B
A
. Show that
det
T
B
=
0
\det T_B = 0
det
T
B
=
0
.
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