Editing Trace class (section)

{{Short description|Compact operator for which a finite trace can be defined}}
{{confuse|text=[[trace operator]], studied in partial differential equations}}
In [[mathematics]], specifically [[functional analysis]], a '''trace-class''' operator is a linear operator for which a [[Trace (linear algebra)|trace]] 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 [[linear algebra]]. All trace-class operators are [[Compact operator|compact operators]]. 

In [[quantum mechanics]], [[quantum state]]s are described by [[Density matrix|density matrices]], which are certain trace class operators.{{sfn|Mittelstaedt|2009|pp=389–390}} 

Trace-class operators are essentially the same as [[nuclear operator]]s, though many authors reserve the term "trace-class operator" for the special case of nuclear operators on [[Hilbert space]]s and use the term "nuclear operator" in more general [[topological vector space]]s (such as [[Banach space]]s).