I don't think that it is helpful to classify basic vs advanced linear algebra according to whether the techniques "scale" to larger data sets. Linear algebra is

I don't think that it is helpful to classify basic vs advanced linear algebra according to whether the techniques "scale" to larger data sets. Linear algebra isn't necessarily about data sets at all. Many of these courses (even this "advanced" one it looks like) completely fail to convey the understanding that vectors and linear transformations on finite-dimensional vector spaces only acquire numerical representations as numerical vectors and matrices when a basis is specified; but that should be part of a basic linear algebra course.