To me this book looks like a whole bunch of equations, with some fancy graphics sprinkled on top. And, far too many equations! Linear algebra is much more elegant (simple) than this. To pick one example, they define the inner product using the cosine of the "smallest angle between the two vectors." Sure if you want to calculate a number (an inner product in two dimensions), and you happened to know the angle in question, this might be helpful. But otherwise it completely obscures everything else about the inner product. How does an interactive graphic help you understand wtf is a cosine doing in this equation? What is a cosine anyway? Where is the graphic for that?
This just seems too backward and over-done to me. But go ahead and test it on some newbies, maybe I'm totally wrong here.
More importantly, the definition of the cosine is given by projecting a unit vector onto a given directed line, and then measuring the length of the projection.
The way to find a given cosine of a given angle between two arbitrary vectors is by taking the dot product of the two vectors and then normalizing by their lengths.
Using the cosine to define the dot product is precisely backwards.
This just seems too backward and over-done to me. But go ahead and test it on some newbies, maybe I'm totally wrong here.