We seriously need better terminology, notation, and pedagogy when it comes to linear algebra. In 2024, such old-style text books just don't cut it anymore.
What, specifically, do you think should be done better? What style of pedagogy do you think would be more appropriate? What notation? What terminology?
Apart from "argument by year number", what's actually wrong with the book?
As far as I know, this notation and terminology is still very standard.
In some ways I like the idea of replacing traditional indexing with something more like the Einstein summation notation, and moving away from the arbitrary feeling that you get around how matrix multiplication is structured, and provide an immediate route into tensor theory.
But so many things that are very important in linear algebra, like matrix inverses, are awkward to express in this notation.
1. What's wrong with this specific book other than that it hasn't been updated in 7 years?
2. What are examples of better terminology, notation, or pedagogy that are improvements over this book? (Doesn't need to be total, could retain the same terminology and notation but just have better pedagogy for example)
I think interactive linear algebra could be superior to a pure textbook. So, a textbook with interactive visualisations that show a concept and allow manipulation. Something like this maybe: https://textbooks.math.gatech.edu/ila/
That does offer slightly better presentation for students with its interactive elements, but otherwise looks pretty standard for an undergrad linear algebra textbook in overall presentation. It has many sections that could use some interactive portion with none at all.
However, I'll give you that interactive texts (or texts with supplemental interactive material) are often better for some things (and some parts of linear algebra) than a plain dead tree format.
