I am eagerly looking for an "Advanced" Linear Algebra text that has exercises that correspond to the contents of William C. Brown's text, A Second Course in Linear Algebra. I am self-studying Advanced Linear Algebra from his book.
I absolutely enjoy studying Brown's book and love his pace. He defines Chain Complexes, Associative Algebra, Tensor Products etc. pretty quick compared to most other texts. This is why I don't want to stop reading this text. But in my experience, while doing so, he doesn't provide "enough" examples and solved problems regarding these new concepts. Thus, while solving his exercises I often feel there're gaps in my knowledge pf these new concepts.
E.g. in Section-$1.5$, he never mentions the term "induced maps" but has an exercise asking us to show something like "one map induces another map". I am totally clueless at these instances as to what I'm really trying to show. The answer to this question is another example.
Thus, I am looking for a textbook with the following criteria :
- The contents and "order of exposition" will be (almost) exactly the same as in Brown's book and also in the same pace. (e.g. getting to Multilinear Algebra and Canonical Forms quicker). But it will fulfill some of the gaps in Brown's concepts.
- (Most Importantly) Doing the exercises of that book would ensure (as much possible) that I am understanding the material from Brown satisfactorily.
I have already looked into the answers to the question High-level linear algebra book. But none of the textbooks there match these criteria. They are either too advanced for me or they have a broadly different ToC than Brown. So, please don't mark this as a duplicate.
