As I have mentioned previously, I intend to self-study relativity and quantum mechanics. As the two pillars of modern physics, the mathematics they employ is also very “modern.” One cannot always rely on the simple patterns used in high school for calculations; therefore, linear algebra is one of the courses I must become familiar with. Currently, as a freshman, linear algebra has not yet been offered, but my view is: “If you need something, you should go learn it, and you will be able to master it.”
In fact, I first encountered linear algebra during the summer after my third year of middle school. The textbook I used then, like many other domestic linear algebra textbooks, adopted a teaching method that required only memorization and calculation. It began with determinants derived from systems of linear equations and then moved to matrices. At that time, I was also memorizing formulas, knowing how to calculate determinants, how they could be used to solve equations, and how matrices were multiplied. However, I had absolutely no idea why things were done that way. I didn’t even understand why the course was called “Linear Algebra.” (Of course, it is also possible that my mathematical level at the time was insufficient.) Many foreign tutorials are well-written and teach in a standardized way, but for an average student like me in China, they often seem too professional. I have always looked for a balance point, but unfortunately, I never found it, so I had to grope my way through various channels.
Meng Yan’s “Understanding Matrices” consists of three articles, the earliest of which dates back to 2006. Although he is not a renowned mathematician and “Understanding Matrices” is not a classic masterpiece, it is undeniable that these three articles played a significant role in my understanding of matrices and linear algebra. Using a geometrically intuitive approach, they allowed me to use matrices clearly for the first time. Of course, “clearly” here does not mean I have mastered everything, but rather that I experienced a sense of “sudden realization” and was “struck with admiration” compared to my previous state. Therefore, I recommend that friends interested in linear algebra read them. While reading special relativity, I used this intuitive matrix approach to derive the Lorentz transformation for the first time in a way that I found satisfactory. In the future, I believe I will frequently experience the wonders of matrices in physics and geometry and understand them more intuitively.
In the future, I may also write some of my own understandings of matrices in the Scientific Space, especially regarding determinants. In fact, Comrade Meng Yan has already explained matrices very well, and with my current level, there is not much I can add. However, he did not discuss determinants, which is a small regret. If I have time, I will supplement that. Meng Yan’s blog has not been updated for a long time; after I have accumulated more knowledge, I might follow in his footsteps and write “Understanding Matrices (IV)”...
Meng Yan’s Blog: http://blog.csdn.net/myan
Download: Understanding Matrices by Meng Yan.doc
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