Earlier quoted context omitted.
Really? I find the part about the SVD in Axler's book extremely unhelpful, big blobs of opaque formulas and jargon with next to no explanation or context that basically require either knowing the topic fully beforehand or a huge amount of effort to parse. e.g. Axler's definition of singular values is the extremely dry and technical: > Suppose T is in L(V, W). The singular values of T are the nonnegative square roots…
From the preface “You cannot read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast. When you encounter the phrase “as you should verify”, you should indeed do the verification, which will usually require some writing on your part. When steps are left out, you need to supply the missing pieces. You should ponder and internalize each definition. For e…
If you are really lucky the result of not explaining things might be an occasional exceptional student who works out a correct personal concept. But more commonly the result is just an unfilled gap in understanding and either a moderately motivated student who develops fluency with symbol twiddling but doesn't get the point of what they're doing or a less-motivated student who decides the topic sucks and gives up.
I've read a lot of linear algebra books, and I personally find Axler's to have average quality exposition and a not tremendously insightful point of view. I know other people who swear by the book though, so YMMV. It's more appropriate for a well prepared pure math student who wants to go to grad school and has a goal of internalizing a lot of jargon so they can read/write pure math papers than for a scientist or computer programmer.