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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'trace'
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trace(AB)=trace(BA) ??? by Johan
Correction id: 3725
Filed on: 2004-03-03 07:43:24
Status: Accepted on 2004-04-05 19:39:58
Type: Addendum
Correction text:
You write "trace(AB)=trace(BA)" under "key formulas for trace operator". Are you considering A,B to be matrices? In that case the statements are obvious (and covered by the entry "trace of a matrix"). If A,B are operators (not necessarily matrices) on some Hilbert space, I believe that the statement "trace(AB)=trace(BA)" is only valid as long as A,B are bounded operators. (Correct me if I'm wrong).
So my suggestion is to make the statements a bit clearer.
/Johan |
Comment from correction handler djao:
It is already specified in the text that $A$ is a matrix, but I added in a clarification anyway. The fact that the statements are covered elsewhere is not a strike against it, since the web site is designed to hold redundant data.
The definition given here assumes the underlying vector spaces are finite dimensional. I don't know the infinite dimensional case well enough to comment. If you wish to add material about the infinite case, that would be great -- please mail me. |
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