Oh yes, +1. Linear algebra is about vector spaces; matrices are a separate topic. Unfortunately, Axler does not define determinant as a volume scaling coeffici

Oh yes, +1. Linear algebra is about vector spaces; matrices are a separate topic. Unfortunately, Axler does not define determinant as a volume scaling coefficient and goes the still arcane way of “(-1)^\deg…” which does not really do justice to the concept. Check out Sergei Winitzki's “Linear algebra via Exterior Products” https://sites.google.com/site/winitzki/linalg https://sites.google.com/site/winitzki/linalg It's free for download and treats determinants in a more geometrically inclined way. BTW, it's written by a physicist, not a mathematician.