tl;dr I am looking for references which cover introductory abstract Linear Algebra but with a programming / computational approach. The only one I found is the Jupyter guide to Linear Algebra
Long version: I am currently teaching Linear Algebra for STEM at a "industry-focused" department for second-term students. We have 7 undergraduate engineering and one "Bachelor of Science and Technology" programs. The general topics which are covered in this course are:
- Abstract vector spaces, subspaces, bases etc.
- Linear maps
- Inner product spaces
- Eigenvalues and diagonalization
(Matrix operations, general linear systems and Gaussian elimination were already covered in a pre-requisite course.)
In my department, this Linear Algebra course (which is common to all programs) has a long problematic history, with high rates of failure, and is seen as quite displaced from the other courses as it is much more abstract. Even as the instructor, teaching it is quite monotonous.
When I took Linear Algebra, as a Mathematics student, it was mostly theorem-proving, which was just right for my goals of becoming a pure mathematician. This has not worked very well for this course.
Considering this (and a few other changes of perspective which I had in the last couple of years), I am trying to incorporate more programming into this course. I adapted some of the more constructive proofs to algorithms, and created a large-ish question bank with questions which necessitate a bit of "engineering" and can be solved programmatically.
This approach has been relatively successful, however I cannot find good references which are appropriate for this approach. Most Linear Algebra references I know either move to Numerical Analysis, focus only on solving linear systems, or are theorem/proof-based.
The only references I have found which move in this direction are:
Practical Linear Algebra for Data Science: From Core Concepts to Applications Using Python, by Mike X Cohen
However, this book focuses on matrices, whereas I am required to follow the syllabus, including introducing the abstract concepts.
Jupyter Guide to Linear Algebra, by Ben Vanderlei
This seems to cover most of what the course requires.
I would like to get more references similar to the ones above (specially the second one), preferably books with physical copies by known scientific publishing companies. References with applications are also welcome (although a bit tangential).