I think these are great points. I justify the lack of some of the fundamental concepts like Gaussian elimination to be due to the fact that the book is meant fo

I think these are great points. I justify the lack of some of the fundamental concepts like Gaussian elimination to be due to the fact that the book is meant for a second course in linear algebra. My copy has dual and quotient spaces and I think these are important topics to get an introduction to if you're looking to learn functional analysis, topology, etc. Some discussion of finite fields could be interesting. This has prompted me to look up linear algebra over finite fields.