Contrast this with climbing a dome: each horizontal foot forward raises you a different amount. Move forward 6 feet, and you’d expect a rise of 2 feet. Imagine a rooftop: move forward 3 horizontal feet (relative to the ground) and you might rise 1 foot in elevation (The slope! Rise/run = 1/3). “Linear Algebra” means, roughly, “line-like relationships”. Without knowing x and y, we can still work out that $(x + y)^2 = x^2 + 2xy + y^2$. Grade-school algebra explores the relationship between unknown numbers. “Algebra” means, roughly, “relationships”. Here’s the linear algebra introduction I wish I had, with a real-world stock market example. It’s the power of a spreadsheet written as an equation. We can take a table of data (a matrix) and create updated tables from the original. Linear algebra gives you mini-spreadsheets for your math equations. The survivors are physicists, graphics programmers and other masochists. Favor abstract examples (2d vectors! 3d vectors!) and avoid real-world topics until the final week.Teach concepts like Row/Column order with mnemonics instead of explaining the reasoning.Name the course Linear Algebra but focus on things called matrices and vectors.Despite two linear algebra classes, my knowledge consisted of “Matrices, determinants, eigen something something”.
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