A non-unital generalized trace and linear complex structures Adam Coffman A basis-free formula for the generalized trace of a linear map between tensor products of vector spaces is proposed which does not refer to scalar multiplication or scalar valued functions. The main application is to real vector spaces with complex structure operators. Erratum: typo on page 535, line 3, should be \vec x_{q^\prime}\mapsto instead of \vec x_{q^\prime}= This is corrected on page 10 of the pfw.edu web site version.