The thing is, you can teach linear algebra as a gateway to engineering applications or as a gateway to abstract algebra. The second one will require a hell of a lot more conceptual baggage than the first one. It’s also what the book is geared towards.
It is also intended for people who know something about the trade; it isn’t “baby’s first book on maths”. (Why can you graduate high school, do something labelled “maths” for a decade, and still be below the “baby’s first” level, incapable of reading basically any professional text on the subject from the last century? I don’t know. It’s a failure of our society. And I don’t even insist on maths being taught—but if they don’t teach maths, at least they could have the decency to call their stupid two-hundred-year-old zombie something else.)
That conceptual baggage is not useless even in the applied context. For example, I know of no way to explain the Jordan normal form in 19th-century “columns or numbers” style preferred by texts targeted at programmers. (Not point at, not demonstrate, not handwave, explain—make it obvious and inevitable why such a thing must exist.) Or the singular value decomposition, to take a slightly simpler example. (Again, explain. You task, should you choose to accept it, is to see a pretty picture behind it.) And so on.
Again, you can certainly live without understanding any of that. (To some extent. You’ll have a much harder time understanding the motivation behind PageRank then, say. And ordinary differential equations, classical mechanics, or even just multivariable calculus will look much more mysterious than they actually are.) But in that case you need a different book and a different teacher.
It is also intended for people who know something about the trade; it isn’t “baby’s first book on maths”. (Why can you graduate high school, do something labelled “maths” for a decade, and still be below the “baby’s first” level, incapable of reading basically any professional text on the subject from the last century? I don’t know. It’s a failure of our society. And I don’t even insist on maths being taught—but if they don’t teach maths, at least they could have the decency to call their stupid two-hundred-year-old zombie something else.)
That conceptual baggage is not useless even in the applied context. For example, I know of no way to explain the Jordan normal form in 19th-century “columns or numbers” style preferred by texts targeted at programmers. (Not point at, not demonstrate, not handwave, explain—make it obvious and inevitable why such a thing must exist.) Or the singular value decomposition, to take a slightly simpler example. (Again, explain. You task, should you choose to accept it, is to see a pretty picture behind it.) And so on.
Again, you can certainly live without understanding any of that. (To some extent. You’ll have a much harder time understanding the motivation behind PageRank then, say. And ordinary differential equations, classical mechanics, or even just multivariable calculus will look much more mysterious than they actually are.) But in that case you need a different book and a different teacher.