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Results tagged with trace
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user 25794
Use this tag when having questions concerning expressions with the trace of a matrix/operator.
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Is there any meaning of tensor contraction?
The contraction $T^i_i$ is simply the trace of this matrix, as you probably also know. For some geometric interpretations of the trace, see this mathoverflow post. … The contraction of $j_1$ with $j_2$ is the trace of this matrix, which is a $\binom {m-1}{n-1}$-tensor as well. …
- 9,444
13
votes
Accepted
Is a partial trace cyclic?
In the partial trace you can cyclically permute factors in the part you are taking the trace over, but not the other part, as follows directly from the definition you gave:
$$\operatorname{tr}_{B}[A_1 … operatorname{tr}[B_1] \ne 0$, we have
$$\operatorname{tr}_{B}[A_1A_2 \otimes B_1] = \operatorname{tr}[B_1] A_1A_2 \ne \operatorname{tr}[B_1] A_2A_1 = \operatorname{tr}_{B}[A_2A_1 \otimes B_1].$$
For the full trace …
- 9,444