Key Machine Learning PreReq: Viewing Linear Algebra through the right lenses

Think Sets and Functions, rather than manipulation of number arrays/rectangles: Linear Algebra is often introduced at the high-school level as computations one can perform on vectors and matrices - Matrix multiplication, Gauss elimination, Determinants, sometimes even Eigenvalue calculations, and I believe this introduction is quite detrimental to one's understanding of Linear Algebra. This computational approach continues on in many undergrad (and sometimes grad) level courses in Engineering and the Social Sciences. In fact, many Computer Scientists deal with Linear Algebra for decades of their professional life with this narrow (and in my opinion, harmful) view. I believe the right way to learn Linear Algebra is to view vectors as elements in a Set (Vector Space), and matrices as functions from one vector space to another. A vector of n numbers is an element in the vector space R n, and a m x n matrix is a function from R n to R m.