This book is written without the assumption that students have taken a calculus course. In making this decision, I hope that students will gain a more authentic experience of mathematics through linear algebra at an earlier stage of their academic careers.
Indeed, a common barrier to student success in calculus is its relatively high prerequisite tower culminating in a course often called “Precalculus”. By contrast, linear algebra begins with much simpler assumptions about our students' preparation: the expressions studied are linear so that may be manipulated using only the four basic arithmetic operations.
The most common explanation I hear for requiring calculus as a prerequisite for linear algebra is that calculus develops in students a beneficial “mathematical maturity.” Given persistent student struggles with calculus, however, it seems just as reasonable to develop students' abilities to reason mathematically through linear algebra.