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 is a extension of a scalar, or a scaler is a special case of a vector. But, they might not know a function is also the extension of a vector. Let's start with such story.