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The word trace has several meanings:

in Linear algebra, the trace of a square matrix A is the sum of its Main diagonal elements. One can also define the trace of a Linear transformation.
in Functional analysis, a trace is a generalization of a trace of a matrix over the orthonormal bases of a Hilbert space. See Trace class.
in field theory, see Field trace.
in semiology a trace is the physical and material result of poietic processes, the "message" made by a "producer" and interpreted by esthesic processes of a receiver (see Esthesic and poietic). It exists and is analyzed on the Neutral level.
in Linguistics, a trace is a notional "ghost" of a syntactic entity that can be regarded as being in an utterance for the purposes of syntactic analysis. It is the result of the movement of a linguistic expression from its position in Deep structure during transformation.
in Deconstruction, a trace is the self-effacing signified that a sign differs and defers from.
in Computer chess, trace is a chess engine.
in Transport a trace is one of two, or more, straps, ropes or chains by which a Carriage or Wagon, or the like, is drawn by a harness horse or other draught animal. This definition results in the saying: to kick over the traces.
in Computer science, a trace is a detailed record of the steps a Computer program executes during its execution, used as an aid in Debugging. One such type of trace is a Stack trace.

See also