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Tr |u><u|v><v| = <v|u><u|v>

In this example the bra <v| seems to have jumped from the end to the start.

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Tr |u><u|v><v| = <v|u><u|v>

In this example the bra <v| seems to have jumped from the end to the start.

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Fredrik

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Fredrik

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Sorry about that. Yes, it's an integer. I should at least have started with this statement: Let ##\{|i\rangle\}_{i=1}^\infty## be any orthonormal basis.

If the Hilbert space is finite-dimensional, replace ##\infty## with ##\dim\mathcal H## (where ##\mathcal H## denotes the Hilbert space). The first step in that calculation is just the definition of the trace of a linear operator.

You may want to also take a look at https://www.physicsforums.com/showthread.php?t=694922 [Broken] about the relationship between linear operators and matrices.

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Fredrik

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