Coding the Matrix: Linear Algebra through Applications to Computer Science
About This Book
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program.
Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications.
Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code.
Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program
Coding the Matrix - Philip Klein 
It used to have a Coursera course, but I think it's been taken down. The website has videos of the course taught at Brown I think.
The associated website is: https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co...
Also, see the Gilbert Strang video series on Linear Algebra:
and the amazing 3blue1brown "Essence of Linear Algebra" series:
A hands on introduction to both Python and Linear Algebra using real world cases (ex. you are given a high res image, make a low res version to put on your website so that it could load more quickly).
- Coding the Matrix, Klein https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co... This has a strong emphasis on LA's utility in CS, and includes concepts outside traditional LA that enrich the narrative.
- Intro to Linear Algebra, Strang https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-S... Strang approaches LA from a practical less-theoretical angle, which makes it very sensible if you're an engineer but may not be as suitable if you're a mathematician.
- Linear Algebra, A Modern Intro, Poole https://www.amazon.com/Linear-Algebra-Introduction-Available... This is a solid text that has worked out most of its bugs over the editions.
- Linear Algebra and its Applications, Lay https://www.amazon.com/Linear-Algebra-Applications-Updated-C... Like Poole, this is also a solid and long running text.
The books by Klein and Strang also benefit from free videos of those courses that are available from Coursera/BrownU and MIT OCW. Klein's is also available on the Kindle.
Book on Amazon, Kindle version $3: https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co...