Definition talk:Trace (Field Theory)

From ProofWiki
Jump to navigation Jump to search

N or T

Here the trace is denoted with $N$, but this is the symbol I've always seen to denote the norm of an element. I suggest to change $N$ by $T$ or $Tr$.--Dan232 15:06, 14 March 2012 (EDT)

$\operatorname{Tr}$ works for me. Anyone else? --prime mover 15:13, 14 March 2012 (EDT)
I like $\operatorname{Tr}$. --Alec (talk) 16:07, 14 March 2012 (EDT)

$\operatorname{tr}$ and $\operatorname{Tr}$ have my preference. --Lord_Farin 17:53, 14 March 2012 (EDT)

Definition page for Trace

Careful here, the redirect page is called Definition:Trace of Linear Operator, but "Linear operator" is defined on $\mathsf{Pr} \infty \mathsf{fWiki}$ to mean a linear transformation from a space specifically to itself, so recommended that, in order to make sure the terminology is completely internally consistent, a rename to Definition:Trace of Linear Transformation may be in order.

If you understand the definition of "linear operator" to be the same as what we have defined here as "linear transformation", then this will of course need to be reconciled. --prime mover (talk) 12:17, 13 July 2017 (EDT)

Good call. The other way around though: The trace of a linear transformation depends on the choice of bases (which is why Definition:Trace (Linear Algebra)/Linear Transformation only defines it for operators), while for linear operators it does not. --barto (talk) 12:38, 13 July 2017 (EDT)
Right okay, so we now have Definition:Trace (Linear Algebra)/Linear Operator which is what I just renamed Definition:Trace (Linear Algebra)/Linear Transformation to, as that's what it is. If someone cares to expand the definition to the general Linear Transformation then no doubt they could do it if they wanted, but for now Definition:Trace (Linear Algebra)/Linear Transformation can be disregarded. --prime mover (talk) 14:23, 13 July 2017 (EDT)
Nice job. I will pay attention to the use of "Operator" and "Transformation" from now on every time I see one. --barto (talk) 14:31, 13 July 2017 (EDT)