Notes on 3Blue1Brown Lectures on the "Essence of Linear Algebra"

I have started season 1 of 4 of 3Blue1Brown's lecture on math. I'll at least go through all of season one and two before going back to the Computer Graphics lessons. If that's the Theory part of my study and I don't have solid foundations I think I'll regret it later.

Vectors | Chapter 1

Vectors are written with [ ] to distinguish them from points ( ).

Numbers, multiplied by vectors, scale them. We can call any number a scalar.

Linear combinations, span, and basis vectors | Chapter 2

Î - "I hat", the unit vector in the X axis.

^j - "J hat", the unit vector in the Y axis.

They are the Basis Vectors of the XY coordinate system.

The "span" is where the vectors can reach.

Linear transformations and matrices | Chapter 3

A Transformation is just a function that describes how to change one vector into another.

"Linear Transformations are a way to move around space such that gridlines remain parallel and evenly spaced, and such that the origin remains fixed."

This one really did it for me, as I recognized the matrix shown from 3D transformations. And it is so simple to think about it as a rotation this way. Î (which describes x) was moved from [1, 0] to [0, 1], and ^J (which describes y) was moved from [0, 1] to [-1, 0]. And now we just multiply a vector by this, and we get a that vector rotated 90º!