"most research is about speeding up calculations on computers"
So, one of the most convenient things that Linear Algebra does is about making things computationally cheap. Without spending too much time since I can't tell if you're a troll :), this branch of mathematics often times provides the easiest way to optimize data of a certain characteristic. People want to save money/time/labor/etc., and a lot of times linear algebra provides the best framework for doing so, and when you have numbers and data on a large scale it often times becomes infeasible to fiddle around with individual cells in a spreadsheet.
RE: relevancy of proofs -- I think a lot of the most interesting and valuable research in this subject is about figuring out mathematical mappings/equivalence of simple LA function to replace laborious procedures in differential calculus and what not. I personally hated proofs when I went through the education system myself, but the value of doing them is to get an abstract and less-biased understanding of things over learning metaphors that may not necessarily apply precisely to any given situation or problem.
(Disclosure: I'm an operations research and math guy doing data science, so bias here.)
So, one of the most convenient things that Linear Algebra does is about making things computationally cheap. Without spending too much time since I can't tell if you're a troll :), this branch of mathematics often times provides the easiest way to optimize data of a certain characteristic. People want to save money/time/labor/etc., and a lot of times linear algebra provides the best framework for doing so, and when you have numbers and data on a large scale it often times becomes infeasible to fiddle around with individual cells in a spreadsheet.
RE: relevancy of proofs -- I think a lot of the most interesting and valuable research in this subject is about figuring out mathematical mappings/equivalence of simple LA function to replace laborious procedures in differential calculus and what not. I personally hated proofs when I went through the education system myself, but the value of doing them is to get an abstract and less-biased understanding of things over learning metaphors that may not necessarily apply precisely to any given situation or problem.
(Disclosure: I'm an operations research and math guy doing data science, so bias here.)