Fundamentals of Linear Algebra and Optimization [pdf]
My test for linear algebra books is how they first present matrices and matrix multiplication.<p>If they define a matrix as an NxM table of numbers with a multiplication operation defined as this complicated formula with a couple of nested sigmas, and then much later a lemma is mentioned that says every linear transformation can be represented as a matrix and then the composition of two transforms is the matrix multiplication of their matrix forms, I throw the book away in disgust. I throw most books away in disgust.<p>This is the second book I've seen that does it right, but unlike the other one [1] this one wraps the very correct presentation of matrices in so much technical language and such a boring cover story that I almost threw it away in disgust anyway.<p>My greatest wish in STEM education is that we teach linear algebra better. It's such low hanging fruit and could change so much!<p>[1] which I saw linked in HN a year ago and don't remember the name of, but it was something like "linear algebra taught the correct way" and was apparently well known in the States so ask your friends