MIT OCW 18.06SC Sections – Lectures & Reading:
- Multiplication and Inverse Matrices
- Strang 2.4 & 2.5
- Factorization Into A = LU
- Strang 2.6
- Transposes, Permutations, Vector Spaces
- Strang 2.7
- Column Space and Nullspace
- Strang 3.1 & 3.2
- Solving Ax = 0: Pivot Variables, Special Solutions
- Strang 3.2
- Solving Ax = b: Row Reduced Form R
- Strang 3.3 & 3.4
- Independence, Basis and Dimension
- Strang 3.5
- The Four Fundamental Subspaces
- Strang 3.6
- Matrix Spaces; Rank 1; Small World Graphs
- Strang 10.1
Hours Spent ~ 75 hours
Summary
I’ve been negligent. The last time I committed a blog entry for math was my first Linear Algebra blog back on January 20. Today is March 1. As I wrote in my last blog, “The Blessing of Love and Longing”, I’ve been inundated – inundated with work and inundated with inner struggle. Consequently, I’ve continued to push the blog writing down the list until “just after I finish _____”.
Looking back, the last time I wrote I barely knew what was going on with Linear Algebra. I had watched the 3blue1brown videos and had the mental twinkle at “what a cool subject this is”. Now, 5 and some odd weeks later I’m not sure I know what’s going on with Linear Algebra, although I’m impressed at how far I’ve come, looking at the list of topics above that I’ve studied.
Because I’ve done so much, I’m not going to even attempt to explain what it is I’ve learned. The topics are there in the bullet points. Describing one of them is tough enough, let alone nine of them. It would take too much time and space, and nobody would want to read it anyhow. Instead, let me share my general thoughts on Linear Algebra as it exists in my mind now.
Linear Algebra is a trip! Calculus challenged my attention to detail and my ability to chain together tools and processes. Linear Algebra, on the other hand, challenges me to conceptualize mathematical relationships. Relationships between vectors and what lies in their spaces. It challenges me to conceptualize how the contents of those spaces, their matrices, and the content thereof, interact with each other. It challenges me to conceptualize the reflective interplay between column spaces, nullspaces, row spaces, and left nullspaces (really, left nullspaces?!). The last topic I dug into began to show how graphs, structures formed by connected nodes, are described with the same matrices.
Linear Algebra challenges me, often to my chagrin, to envision what the structures or relationships “look” like given a set of conditions, to describe their ranks, dimensions, and bases. To understand how pivots and free variables determine the manifestations of matrices. Maybe that’s what really stretches the mind, that we are rarely dealing with a single definite mathematical entity, e.g. number, equation, integral, etc, but a potentiality.
I struggle with Linear Algebra. I want to feel very confident that I understand the topics I work through, but often the understanding doesn’t come until I’ve moved on to struggle with a new topic. Understanding is latent. This course will take some time. I’ll give it the time it deserves. I feel like Linear Algebra is really changing how I think. I’ll do my best to exercise greater diligence with my blog writing, but can’t guarantee I’ll be as consistent as I was before. My business is at peak urgency right now. Nevertheless, if I lag, be assured it’s not because I’ve stopped studying. Every day I rise and rack my brain with it. Thanks for bearing with me.