Well, if I understand your point you are refering to the fact that in many high level programming languages, the language itself is able to dected the most effi

Well, if I understand your point you are refering to the fact that in many high level programming languages, the language itself is able to dected the most efficient method to do solve some linaer algebra problems, say solving linear systems. However QR factorization (or other factorizations) may be usefull when you have to solve different problems but with the same matrix, so that factorizing once and for all gives you an advantage (for example many undetermined linear problems [1]). In this case knowing something about factorizations, or what to use when, may be helpful [1] https://en.wikipedia.org/wiki/QR_decomposition#Using_for_solution_to_linear_inverse_problems https://en.wikipedia.org/wiki/QR_decomposition#Using_for_sol...