Trace (linear Algebra) - Generalization

Generalization

The concept of trace of a matrix is generalised to the trace class of compact operators on Hilbert spaces, and the analog of the Frobenius norm is called the Hilbert–Schmidt norm.

The partial trace is another generalization of the trace that is operator-valued.

If A is a general associative algebra over a field k, then a trace on A is often defined to be any map tr: A → k which vanishes on commutators: tr = 0 for all a, b in A. Such a trace is not uniquely defined; it can always at least be modified by multiplication by a nonzero scalar.

A supertrace is the generalization of a trace to the setting of superalgebras.

The operation of tensor contraction generalizes the trace to arbitrary tensors.