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Chapter 7: Commutators and Anticommutators
https://doi.org/10.1142/9789813143807_0007Cited by:0 (Source: Crossref)
Abstract:
Let A and B be n × n matrices. Then we define the commutator of A and B as
[A,B] := AB − BA.
For all n × n matrices A, B, C we have the Jacobi identity
[A, [B,C]] + [C, [A,B]] + [B, [C,A]] = 0n
where 0n is the n × n zero matrix. Since tr(AB) = tr(BA) we have
tr([A,B]) = 0.
