To add a little on different terminologies being a feature: if you ultimately want to apply linear algebra, you’ll have to build a bridge from the theory to the particular application that is probably even more difficult than the bridge between two presentations of the theory. So it’s probably good to practice building bridges.
(I’m also suspicious of people who say that the last book that they read on a subject was the best book, because that’s when it clicked. How much did the first books prepare them?)
To add a little on different terminologies being a feature: if you ultimately want to apply linear algebra, you’ll have to build a bridge from the theory to the particular application that is probably even more difficult than the bridge between two presentations of the theory. So it’s probably good to practice building bridges.
(I’m also suspicious of people who say that the last book that they read on a subject was the best book, because that’s when it clicked. How much did the first books prepare them?)