Linear Algebra, Part 1

This week I parsed through the subject of Linear algebra to do some meta-learning and find available resources. I settled mostly on the Gilbert Strang lectures on MIT Opencourseware and on an old Linear Algebra textbook by David Lay (see resources section). After some high level overview the following seem like core aspects of scope:

1. Vectors, Matrices, and Spaces/Subspaces

2. Systems of equations and Linear Algebra bases solutions

   1. Gaussian Elimination (row reduction)

   2. Matrix Inversion

   3. LU Decomposition

3. Determinants

4. Linear Transformations

5. Eigen Vectors and Eigen Values (probably the high point for what I’m going to need)

6. Span, Basis

7. Row Space, Column Space, Rank

I covered the first couple lectures from MITOCW, and made some notes that I’ll post on Instagram for this week. One thing that struck me, that I either missed or don’t remember from college, is that the row picture and the column picture of an Ax=b equation are actually completely different spaces - one using the x vector components as axes and the other using the column components as axes.