Lx=d: SundayResearch

Scalar, vector, and function Scalar When I want to mention a quantity, I use numbers. A number always represents ``something.'' For example, if I said 130, what is this number means? The number itself has not so much meaning. This could be someone is 130cm tall, or Autobahn's speed limit is 130km/hour.  One number represent ``something'' e.g., ``tall cm'', ``speed limit km/hour.''  Figure 1 shows this. These single numbers are Scalers. It is just a number, why it has a special name Scalar? I think this is just for distinguishing a scalar and a vector (or a (complex) number). Figure 1 Scalar has some meaning Vector There are many stuffs I can not represent with a scalar. For instance, a place. The distance from my apartment to Zoo station can be represented by a scalar value. But, if you need a direction, I can't tell it by a scalar value. I could say, 50 degree from the north in clockwise direction, the distance is 5 km. Or go north 3...

Introduction There was a famous mathematician and computer scientist, Richard Hamming. I am reading his book, Digital Filters. I would like to write  something I understand about this book. Let's talk about eigenvalue and transfer function. But this is too sudden. Most of the people (including me) would say What is eigen-blah stuff? Therefore, I would like to start why it matters, what is the motivation to think about that, as usual in my blog. After reading some math book, I often said, ``I don't understand'' or ``So what?'' I want to say, ``Wow, that's great.'' If I said, ``Wow, that's great,'' then I usually understand what the purpose is and it is achieved in the paper. I try to explain this in the high school math only, but, I found out one step is missing. That is the relationship among scaler, vector, and function. I would like to explain these are all the same in some abstraction sense. Maybe high school students know a vector...