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 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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