I am a pure math major. I am taking a one-semester course covering the following topics:
Inner Product Spaces,
Direct Sums of Subspaces,
Primary Decomposition Theorem,
Reduction - (triangular, Jordan, rational, classical),
Orthogonal Direct Sums,
Our lecturer is a number theorist so he will probably make some links with number theory. He does not recommend any textbooks for the course but I learn best alone out of books designed for self-study. Lecture theaters full of whispering and distractions are hell to me! I like books that are written in a personal, quirky style that prompt deep reflection and encourage independent thinking. I like colorful motivating material!! I dislike mention of any "real-world applications" (ie physics/engineering). I hate when writers leave out big chunks in proofs and say the missing steps are "trivial" when they are not. I like it when solutions are available to the exercises.
Thank you for your help :)