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If A and B are symmetric matrices, show that their commutator is antisymmetric [see equation (6.3)].

If A and B are symmetric matrices, show that their commutator is antisymmetric [see equation (6.3)].

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equation (6.3) defines the commutator of two operators, A and B. It is expressed as: \[ [A, B] = AB - BA = \text{commutator of A and B.} \] This mathematical expression describes the difference between the product of A followed by B, and B followed by A. The commutator is an important concept in various fields such as quantum mechanics and algebra, where it is used to determine the extent to which two operators do not commute, i.e., the result of their application depends on the order in which they are applied.
Transcribed Image Text:Equation (6.3) defines the commutator of two operators, A and B. It is expressed as: \[ [A, B] = AB - BA = \text{commutator of A and B.} \] This mathematical expression describes the difference between the product of A followed by B, and B followed by A. The commutator is an important concept in various fields such as quantum mechanics and algebra, where it is used to determine the extent to which two operators do not commute, i.e., the result of their application depends on the order in which they are applied.
If A and B are symmetric matrices, show that their commutator is antisymmetric [see equation (6.3)].
Transcribed Image Text:If A and B are symmetric matrices, show that their commutator is antisymmetric [see equation (6.3)].
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