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Arnold's Trivium
1991 Arnold's Trivium
90
Problem 90
Problem 90
Source:
July 1, 2010
linear algebra
matrix
Problem Statement
Calculate the sum of matrix commutators
[
A
,
[
B
,
C
]
]
+
[
B
,
[
C
,
A
]
]
+
[
C
,
[
A
,
B
]
]
[A, [B, C]] + [B, [C, A]] + [C, [A, B]]
[
A
,
[
B
,
C
]]
+
[
B
,
[
C
,
A
]]
+
[
C
,
[
A
,
B
]]
, where
[
A
,
B
]
=
A
B
ā
B
A
[A, B] = AB-BA
[
A
,
B
]
=
A
B
ā
B
A
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