I agree with you. My teacher at Czech Technical University had a similar, abstract approach to linear algebra - also used linear operators all the way, matrices

I agree with you. My teacher at Czech Technical University had a similar, abstract approach to linear algebra - also used linear operators all the way, matrices were only mentioned in passing (and in exercises). It was a tough course for 1st year freshmen (almost as difficult as mathematical analysis), due to its abstract nature, but I was grateful for that in the end.