Anon11/17/25, 11:21No.16850486
I highly, HIGHLY recommend Gaitsgory's notes on Algebra I (Math 122) and Algebra II (Math 123). They lay out the theory clearly, what matrices actually are, what linear transformations are, etc. Most books have no clear distinction between application and theory and end up presenting those concepts in a really confused matter. You shouldn't have to do a full course on group theory and commutative algebra before seeing a single vector space but clearing up what those structures are before moving on to more complex structures like a vector space helps a lot with getting used to the formalism.
Also, it's just notes and thus doesn't have many examples, but I still highly recommend you read through them as a lucid treatment on just the theory, feel free to supplement other texts for exercises and examples (the notes actually have exercises too with solutions to a lot of them but they're not really focused on computational stuff).