I was wondering if there was an intuitive way to think about determinants of matrices that represent linear transformations in abstract vector spaces over arbitrary fields.

There are many posts about the intuition for the determinent of n-tuple spaces over the field of real numbers where they represent how the volume of the shape outlined by the basis vectors change and about how the determinant is negative should two basis vectors "flip about". There is lots on this here: What's an intuitive way to think about the determinant?

However I am wondering how the idea of a determinant generalities to more abstract vector spaces over arbitrary fields. Does it actually mean something intuitively or does it just become some computation. I suppose that a larger determinant simply means that the basis vectors are transformed to carry more "magnitude" of some sort. More importantly what would it mean to have a negative determinent in this context, i.e. for the basis vectors of a more abstract space such as that of polynomials to "flip about" as they would for classical n-tuple vectors.

What is the best mindset to approach this topic as I am learning it?