Trace class

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, specifically <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a>, a trace-class operator is a linear operator for which a <a href="/facts/Trace_(linear_algebra)/dchFFvHt">trace</a> may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>. All trace-class operators are <a href="/facts/Compact_operator/KNkcK4mE">compact operators</a>. 
In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, <a href="/facts/Quantum_state/7jbxd7Dx">quantum states</a> are described by <a href="/facts/Density_matrix/A1XdylJa">density matrices</a>, which are certain trace class operators. 
Trace-class operators are essentially the same as <a href="/facts/Nuclear_operator/kxnx5bIJ">nuclear operators</a>, though many authors reserve the term "trace-class operator" for the special case of nuclear operators on <a href="/facts/Hilbert_space/aDFMh4lV">Hilbert spaces</a> and use the term "nuclear operator" in more general <a href="/facts/Topological_vector_space/XRex1ChN">topological vector spaces</a> (such as <a href="/facts/Banach_space/sDEIk7EC">Banach spaces</a>).

Trace class open-in-new

Trace class