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This is my understanding. The basic idea of a matrix with rows and columns may be the X-Y axis, which means a 2-dimensional space. So we generously divided the rows and columns into two parts. If you are more interested in the relationship between rows (such as the X axis you are interested in), you will get your point of view from the perspective of the X axis. In other words, you can imagine that you are just standing at a certain position on the X axis from the origin to the positive X axis (note: the X axis is a space of 1 dimension), and you prefer to use the solution of 1 dimension to solve your problem. Don't worry! Let me describe it more vividly.

The problem lies in two-dimensional space, and you want to solve it from the perspective of 1 dimension. Why (question 1)? How can we do it (question 2)? The answer to the question 1 is that, from our experience and conclusion, it is easier to solve than a two-dimensional problem in most cases. The answer to question 2 is more complicated. Matrix is a clever way to compress a two-dimensional problem into a 1 dimensional problem. Of course, the method is to divide the branches and columns. You can continue to imagine that you are standing on the X axis and ready to solve the problem you are facing from a 1 dimension perspective. No matter what happens on the Y axis, you have successfully ignored the Y axis, because you have no ability to meet anything in the second dimension (Y axis). This is a simple way to solve the problem.

Pause question 2:)

Referring to Figure 1, imagine a compressor compressing a square biscuit in one direction.

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You are more interested in the x axis, and don't care what is added on the y axis. Well, in fact, some solvers think that they first consider that each column contains homogeneous elements and that columns can be compressed. Later, we used the method of dimension reduction by compression (I named it CDDM). Refer to fig. 2.

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Because of this, you are more likely to go from point O (0,0) to point A (0,a) on the X axis, where' a' is a real number on the X axis, and you are considering a 1 dimension problem. Referring to Figure 3, you will see how we have replaced and simplified this problem.

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Do you have compression dimension reduction method? Let me summarize it briefly. Matrix is a two-dimensional problem. We use CDDM to simplify, that is, select rows or columns to calculate and prove a theorem or problem. I think this method may reduce the dimension. The rule is that we believe that each row or column has corresponding attributes for each element contained in each row or column.

Yes, the matrix is a container! If you are more interested in row relationships and imagine walking on the x axis, you will think that there are no columns, so you will compress the columns into a single element. Then, you go from the origin O (0,0) to the point A (0,a), where "A" is a real number on the X axis. It's easier to find the row relationship in the matrix, isn't it?

Now, I suggest you reconsider the form of the matrix in Figure 4. Why do we write like this?

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I wish I could explain question 2 more clearly. But, you know, English, as a second language, is not very fluent for me. Finally, I want to emphasize that rows and columns are the same, and I think this is the main relationship between rows and columns. The only difference is the way we solve problems and the way we understand knowledge. CDDM is a useful attitude in our real life.