Let $k$ be a field and let $V$ be a finite dimensional $k$-vector space.
Let $\Lambda_* : k \text{-vect} \rightarrow k \text{-alg}$ be the exterior algebra functor, whose target is associative $k$-algebras and whose cotarget is finite dimensional $k$-vector spaces.
There is a "graded trace map", where, for $f : V \rightarrow V$ a map of $k$-vector spaces, we can define $\text{tr}_* \left( \Lambda_* f \right)$ as an element $\sum_{i \geq 0} \text{tr} \left( \Lambda_i f \right)(- t)^i$ of $k[[t]]$.
I'm wondering where I can read about this. I am also wondering where I can read about linear algebra like it.