After talking about this issue last lecture with you in front of the blackboard and being prepared for any feedback (although none given - -), I understood the issue more to details than before.
Since my understand of what the powers of the Matrix donates and why it is was all presented in the class so in this blog I want to talk about some other thinking about it.
In X, there are some elements showed as "-", which means undefined. But when doing calculations of X, "-" is calculated just as "0". So at first there were some seconds when I was puzzled why use such a strange sign instead of defining it as zero directly? Indeed that's more like a matrix than that with some "-"s, isn't it?
Not until when I tried to explain the issus I explained to you last lecture that I understood it better. In my opinion, elements in X not only shows whether two points are combined, but also suggest a corresponding
relation. That's about what I said before in the class, when and only when two elements of the same location in the row vector and column vector has the same non-zero value can we get a non-zero result. So maybe I shouldn't say that "-" is calculated just as "0". "-" still has its own calculation function, and it just can't contribute new variables to the result.
Still in X, all the meaningful and non-zero elements have the same power: 1. Why is it?
I have three ideas about this question.
1. The first idea comes from the first glance at the matrix. Just as the old thinking in the binary system: 1 represents "there be" and 0 represents "there not be". And a point doesn't need to reach itself so it's "-", undefined.
2. The second idea comes from the conclusion of the meaning of the powers of a matrix. 1 shows two points are combined. And what's more, since in X, we only have one step to take, so if we can and we want to reach another point, we can only go for it directly, no other ways. So the elements can't have other values than 1.
3. The last idea comes from the process I tried to explain the reason of the meaning for the powers of a matrix. Since all the calculable elements have the power of 1, all the variables added to the result of an element in X.^2 is 1. How many 1s are added here corresponds to the number of middle points here. Only with such defination can we have the wanted effects in X.^2, or X.^n (n>=2).
That's some of my thinking about the powers of a matrix in SNA.
Hoping for more ideas ~~~
After reading the article I have a deep understanding of Powers of a Matrix, especially, and the element -. Just as you said, the element in X not only shows whether two points are combined or not, but also suggests a corresponding relationship. However, I still feel confused about it when doing the calculation. The value of element - would be zero or others. I’m sorry I cannot get your point. Would you explain it in an easier method?
回复删除e...I mean when doing the calculation, "-" has its own fuction, not as zero or others. Only when two elements of the same place in the row vector and the column vector has the same value can there get a varibles added to the result. But "-" multiplied by "-" is still none so no effect is added to the result. That's what makes "-" seem like zeros in calculation. That's all my own thinking, maybe not too serious ...
删除The powers of the matrix is meaningful.Yeah~ as we know in the lecture, X^n means the how many ways to reach some point in N steps. Do you think about what does it help to analyze social network? Do you remembers there are three correlation matrix multiplication in the lectures, what does it mean? Maybe we can talk more about it....
回复删除Thank you for your reply ~ In fact I wanted to talk about powers of the three correlation matrix multiplication in this blog. But the first part takes so long words and it was too late so I deleted the last two ... I will wrote them back someday and I hope to talk more about it with you ~
删除Um... I also got confused when dealing with the "-" thing and finally I just consider it undefined and skip all calculation related.
回复删除Thank you for your analysis about the matrix.
回复删除From your article, I study more about the matrix calculation rule about the matrix.
As you said in your blog, "-" is just calculated as the "0" but I don't think it is the same to "0". It just is similar to "0". And actually it has some difference from "o", no matter in calculating and function aspects.
So if we want to utilize the matrix correctly, we must know the meaning of all the elements of the matrix, such as X, -, 0.
Mathematics can be applied to analyse models in different field and finally we will find a good combination between them.
回复删除For your last thinking, since 0 and 1 can be the most basic numbers in the world of math. they can always contain most information.
Your blog shows me a new picture about such combination.
Thank you!
As your article shown that mathematics is very useful to analyze different models about social networking. Your article tells us how to use the simple I and o to solve the problem, and I suggest that you could make a chart to show your findings, that will be perfect!
回复删除Agree with you about the idea of the matrix calculation does not consider about zero and undefinable value "-".
回复删除I was also wondering about this question... "-" and "0" are regarded as different things but when calculating they act as the same role. Thanks for your such a detailed /Epistemic Cognition/ shared XD
回复删除It seem that "-" is not easy to understand when most of people contact this concept for the first time. But your blog gives us a very helpful explanation of it. "-" really has its special role function.
回复删除"How many 1s are added here corresponds to the number of middle points here. "
回复删除------------------------------
I think that's exactly the meaning of the calculation process in this example. Thank you for sharing.