Here is a direct link to the page in the preview of the book where the matrix-product-is-the-same-as-linear-transformation idea first appears: https://minireference.com/static/excerpts/noBSguide2LA_previ...

I can't quite tell if the book passes the test, since the entry-point is the definition of matrix-vector product which is very close to a "complicated formula with a couple of nested sigmas" but the book also mentions the notion of matrix representations, so hard to tell overall.