In mathematics, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev...
27 KB (4,663 words) - 05:44, 30 September 2024
size. Thus, similar matrices have the same trace. As a consequence, one can define the trace of a linear operator mapping a finite-dimensional vector space...
37 KB (5,493 words) - 10:51, 23 October 2024
specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent...
18 KB (3,186 words) - 06:46, 15 October 2024
partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function...
11 KB (2,047 words) - 22:14, 26 May 2024
Look up Trace, trace, traces, or tracing in Wiktionary, the free dictionary. Trace may refer to: Trace (Son Volt album), 1995 Trace (Died Pretty album)...
4 KB (569 words) - 18:00, 6 July 2024
matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matrices. Let H n...
26 KB (4,516 words) - 21:37, 13 August 2024
In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence...
3 KB (378 words) - 07:20, 23 April 2023
Matrix norm (redirect from Trace norm)
which is the operator norm induced by the vector 2-norm (see above). Finally, p = 1 yields the nuclear norm (also known as the trace norm, or the Ky...
26 KB (4,514 words) - 08:26, 9 October 2024
product of two Hilbert–Schmidt operators has finite trace-class norm; therefore, if A and B are two Hilbert–Schmidt operators, the Hilbert–Schmidt inner product...
9 KB (1,391 words) - 06:35, 19 October 2024
(\varepsilon ^{T}\Lambda \varepsilon )} . Next, by the cyclic property of the trace operator, E [ tr ( ε T Λ ε ) ] = E [ tr ( Λ ε ε T ) ] . {\displaystyle...
6 KB (969 words) - 00:01, 31 July 2024