While pursuing the analogies between some branches of mathematics and some fields of linguistics, I have recently come across the idea of intermediate trace, which, in the framework of the study of language (particularly, of syntax) is supposed to mean a trace which has to be erased at some further point of the derivation, in order not to block the whole, which would result in no real output. The technical reasons for this are a little dull for people not familiar with the field, so I ignore them for the time being. I know that in maths a trace is basically the constant value of the sum of the diagonal entries of a square matrix, irrespective of changes of basis. It can also be extended to tensors and the like, it appears. My question is then quite simple: Do you know of intermediate traces in mathematics (preferably in matrix and / or tensor domains)? If so, which are their main features? Thanks in advance.
PS: These 2 links might be helpful for you: http://en.wikipedia.org/wiki/Empty_category_principle http://en.wikipedia.org/wiki/Trace_%28linguistics%29