Intuitive

Linear algebra gives you mini-spreadsheets for your math equations.

We can take a table of data (a matrix) and create updated tables from the original. It’s the power of a spreadsheet written as an equation. An Intuitive Guide to Linear Algebra by Kalid Azad

Concrete

• A great introduction is An Intuitive Guide to Linear Algebra by Kalid Azad
• For a quick introduction, see https://minireference.com/static/tutorials/linear_algebra_in_4_pages.pdf
• and http://www.cns.nyu.edu/~eero/NOTES/geomLinAlg.pdf which explains really nicely many linear algebra in geometric terms.
• For a nice guide, see How to Self-study Algebra: Linear Algebra
• https://graphicallinearalgebra.net
• immersive linear algebra by J. Ström, K. Åström, and T. Akenine-Möller (free online book)
• Essence of Linear Algebra video mini-series

Good books are:

• Linear Algebra Done Right by Sheldon Axler - despite the title a great book.
• Linear Algebra Done Wrong by Treil - even better than Linear Algebra done Right.
• No bullshit guide to linear algebra by Ivan Savov
• Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by John H. Hubbard and Barbara Burke Hubbard - Extremely student friendly, lots of margin notes that talk about the "soft" stuff that's so crucial to the actual practice of math. Reading just the margins jumps your mathematical maturity by 2 years.

A nice video introduction is

• Essence of linear algebra by 3Blue1Brown

Abstract

Why is it interesting?