> After watching this and having read the comment, I am quite puzzled by the approach American seems to take to linear algebra. Are matrices viewed as the core of the subject in the USA ?

The US is a very big place. I doubt there is an american approach to linear algebra. We really don't have a single approach to anything. Different schools and majors probably approach the topic differently. My college had a linear algebra course specifically crafted for CS majors and engineers. I took that and it did focus on matrices. It was also the only math class that required programming. I believe math majors had their own linear algebra course.

> My country curriculum introduces linear algebra through group theory and vector spaces. Matrices come later.

Different strokes for different folks. If it worked out for you that's all that matters.