Main Page | See live article | Alphabetical index A bounded linear operator A over a Hilbert space H is said to be in the trace class if for some (and hence all) orthonormal bases Ω of H; the sum is finite. In this case, the sum is called the trace of A, denoted by tr(A) and is independent of the choice of the orthonormal bases. When H is finite-dimensional, then the trace of A is just the trace of a matrix and the last property stated above is roughly saying that trace is invariant under similarity. The trace is a linear functional over the trace class, meaning The bilinear map <A,B>=tr(AB*) is an inner product on the trace class, where the induced norm is called the trace norm. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.