Authors in a Markov matrix: Which author do people find most inspiring? (2)

Problem statement: Analyzing author relationships (1)

Let's start thinking about what is the problem.

One of my friends who studies literature asked me how I would analyze the relationships between authors. For instance, ``How can we measure the influence of Shakespeare in English literature compared to other writers?''

The discussion of which literary works are canonical and the attempts to define the boundaries of the canon are endless (http://en.wikipedia.org/wiki/Western_canon). Typically, a specific individual or group has defined the boundaries of the canon. If we consider creating a ranking system using numbers, I wouldn't even know how to begin such a discussion. It is easy to imagine such discussions raising an even more generic question: ``What is art?'' Answering that question is clearly beyond my ability!

If nobody can agree on such a ranking system for authors, I could at least start by creating an incomplete definition, hoping to improve it later. However, my definition would only reflect my personal taste. We could extend the result of one person's opinion to many people's opinions by asking a lot of people. We could start by assuming that there is a correlation between the most frequently printed book and the most preferred book. If this is true, we can just check the number of printings of a particular book. Simple web search tells us that the two most printed books are IKEA's catalog (http://en.wikipedia.org/wiki/Ikea_catalogue) and the Bible. I doubt that the most influential book for English literature is IKEA's catalog. My intuition says maybe not. ``What is literature?'' is also not a simple question. We could replace the number of printings with the total sales, but then magazines and newspapers would have quite a large influence. But again, I am not so sure that this is what my friend and I are looking for.

It seems problem is not so simple, where can I start?

Comments

Why A^{T}A is invertible? (2) Linear Algebra

Why A^{T}A has the inverse Let me explain why A^{T}A has the inverse, if the columns of A are independent. First, if a matrix is n by n, and all the columns are independent, then this is a square full rank matrix. Therefore, there is the inverse. So, the problem is when A is a m by n, rectangle matrix. Strang's explanation is based on null space. Null space and column space are the fundamental of the linear algebra. This explanation is simple and clear. However, when I was a University student, I did not recall the explanation of the null space in my linear algebra class. Maybe I was careless. I regret that... Explanation based on null space This explanation is based on Strang's book. Column space and null space are the main characters. Let's start with this explanation. Assume x where x is in the null space of A . The matrices ( A^{T} A ) and A share the null space as the following: This means, if x is in the null space of A , x is also in the n...

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs. https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF I like this article about naming of math by Kalid Azad. https://betterexplained.com/articles/learning-tip-idea-name/ Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too. Explanation: why -1 * -1 = +1 by pattern https://youtu.be/uD7JRdAzKP8 Explanation: why -1 * -1 = +1 by climbing a mountain https://youtu.be/uD7JRdAzKP8 But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178 . Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar um...

Why parallelogram area is |ad-bc|?

Here is my question. The area of parallelogram is the difference of these two rectangles (red rectangle - blue rectangle). This is not intuitive for me. If you also think it is not so intuitive, you might interested in my slides. I try to explain this for hight school students. Slides: A bit intuitive (for me) explanation of area of parallelogram (to my site, external link) .

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