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For questions about trace, which can concern matrices, operators or functions. If your question concerns the trace map that maps a Sobolev function to its boundary values, please use [trace-map] instead.

In the context of linear algebra, the trace of a square matrix $M$ is the sum of the diagonal entries.

It's almost the same idea in the case of operators on a separable Hilbert space (with conditions of convergence).

In the context of partial differential equations, when we work with an open set having good conditions, we can define what we call a trace operator.

Use it with the appropriate tags.