200906Japan 7.6-8.6

6/7

I read "Ginga Hitchhaiku Gaido" (Hitchhiker's guide to the galaxy) Douglas Adams. I have read it in English, but I might miss something, so I read this again in Japanese. But, it was so fun in English, it is not so fun in Japanese. But translation seems OK. The book is very difficult to translate, I presume.

I read "The Rules" Ellen Fein and Sherrie Schneider.I see some of the rules. But in my case I give up such a woman. Maybe many of men will not give up and also I should not? But I think it is better to give up and move on.

6/8

Today I visited to Shizuoka and close Sumitomo bank account. This bank has no branch in my city, so it is a bit inconvenient. But around 2000, according my research, I believed this bank was the most convenient bank from outside of Japan.

By the way, I found a nice shop called Yumekoubou in the city. This shop's clerk has a nice accessory and I asked where can I get. Then she introduced me a shop called Ernie Pyle Company & Garden (picture). This shop is amazing.

There is a small park in the city. There is an intermittent convolution (picture). There are some more interesting objects in the city.

I read "Deadeye dick" Kurt Vonnegut. This is fun, but I do not understand why it is so fun. It is easy to read... I like these black wit and warm talk but sometimes includes a small rejections. Maybe this is totally stupid idea, but I feel sometimes Murakami Haruki. They are totally different, but I feel something common at the bottom, a little bit. I love both authors.

Comments

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) .

Geometric Multiplicity: eignvectors (2)

If eigenvectors of a matrix A are independent, it is a happy property. Because the matrix A can be diagonalized with a matrix S that column vectors are eigenvectors of A . For example, Why this is a happy property of A? Because I can find A's power easily. A^{10} is not a big deal. Because Λ is a diagonal matrix and power of a diagonal matrix is quite simple. A^{10} = SΛ^{10} S^{-1} Then, why if I want to compute power of A ? That is the same reason to find eigenvectors. Eigenvectors are a basis of a matrix. A matrix can be represented by a single scalar. I repeat this again. This is the happy point, a matrix becomes a scalar. What can be simpler than a scalar value. But, this is only possible when the matrix S's columns are independent. Because S^{-1} must be exist. Now I come back to my first question. Is the λ's multiplicity related with the number of eigenvectors? This time I found this has the name. Geometric multiplicity (GM): the number of in...

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...

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