After dinner, he returned to the library again, and it was usually the time for Qiao Ze to help Su Mucheng explain the problem.

Watch the teaching video for an afternoon, and the questions you don't understand will be explained in this time period.

Today there is one more beneficiary - Chen Yiwen.

For Joze, it's not a burden.

Explaining these simple basic concepts is just the right time to relax your brain.

……

"Just ask." As soon as the three of them were done, Chen Yiwen heard Qiao Ze simply say these two words to Su Mucheng, and then looked at the two unconsciously.

Su Mucheng, who had been feeling that she hadn't paid much attention in the afternoon, also became serious and pushed the notebook directly between her and Qiao Ze. Then the whole head poked over: "Qiao Ze, I didn't understand the linear algebra matrix dimensionality reduction judgment too much today, it seems to be different from what is taught in the textbook we studied?" ”

"Show me the textbook too." José said.

Su Mucheng found the textbook from his schoolbag and handed it over.

Qiao Ze looked at the catalog, flipped through a few pages casually, and said, "Understood." ”

Then he asked, "What is the essence of the matrix?" ”

Su Mucheng replied: "Function? ”

"To be precise, it's a function that manipulates vectors. ”

Su Mucheng nodded.

"What does it do?"

"Conversion and scaling, but what does this have to do with dimensionality reduction? Is a 2D vector rotation and pull-up still a 2D vector? ”

"This is the point of view in the textbook, the matrix only acts on a vector alone, and this learning effect is biased towards teaching you how to do the problem in the simplest way. But in fact, the more cutting-edge view in mathematics is that matrices are transformations that can act on the whole space. During the transformation process, the single vector you observe will be deformed with the deformation of space. ”

"Huh?" Su Mucheng listened more seriously.

Qiao Ze picked up the pen and paper and began to explain.

"Understanding this concept, you look at this special matrix, let's use this matrix to operate this two-dimensional space, which can also be understood as manipulating all the points in the two-dimensional space, you see, after the operation, the area of the whole space is equal to 0, which means that the space is compressed into a straight line."

"Isn't this a two-way foil?" Su Mucheng said in surprise.

Qiao Ze frowned and asked, "What is a two-way foil?" ”

"Huh? Haven't you seen the three-body problem? ”

When Su Mucheng explained the anti-heaven weapon of the two-way foil clearly, Qiao Ze shook his head.

"Although dimensionality reduction matrices do have applications in physics, they are mainly in the quantum dimension and have no effect on the macroscopic. In addition, the correct mathematical expression is that under the dimensionality reduction matrix operation, a subspace of the two-dimensional space is mapped to the zero-degree space, which is the concept mentioned in the textbook, the core. ”

Su Mucheng nodded thoughtfully.

"It's the same from 2D to 1D, from 3D to 2D, or 4D to 1D. The question now is how to determine the dimensionality reduction matrix. There are two methods, the simpler one is the determinant; The other is by comparing rank to dimension. Furthermore, you can also think about algorithms based on tangent space discriminant manifold dimensionality reduction matrices. ”

Qiao Ze patiently explained, just talking, although the speed of speech did not change, and the speed of his hand that kept writing on the manuscript paper did not change, but his brows suddenly wrinkled slightly.

Seven points of attention was listening carefully to the explanation, and Su Mucheng, who was still paying attention to Qiao Ze, immediately noticed Qiao Ze's slight movements, and asked suspiciously, "What's wrong?" ”

"I suddenly realized that my mind was stuck in a strange circle and I was only thinking about using the group theory method to build a framework," Jozer said. But in fact, the thinking can be completely liberalized, and we can use a more concise mathematical way to make the machine complete the corresponding mapping of change and invariance. I've got an idea. ”

"That's right, then that's the process I've written down. You only need to draw a few diagrams, compare the determinant algorithm with the matrix space operation, and specify the area composition of the unit, then you can understand the dimensionality reduction matrix. ”

After speaking, Qiao Ze pushed a large piece of manuscript paper to Su Mucheng, then looked up at Chen Yiwen, who was looking at the two of them blankly, and said, "Chen Yiwen, you continue to look down first, if there is any problem, I will revise the framework drawn up in the afternoon." That's right, find out as soon as possible. I think your work might be about to start. ”

Then Qiao Ze took his laptop and devoted himself to his research again.

Chen Yiwen was already dumbfounded.

So is this the efficiency of self-study? What have you learned about this? Why is it all that he doesn't feel like he's been exposed to?

Then there was a little grievance.

I said that I would give him a lecture in the evening.

Forget it, hey......

Abominable Gender Dominance! Destroy humanity!

Thinking so in his heart, Chen Yiwen still couldn't help but look at Su Mucheng and asked softly, "That...... Where have you learned linear algebra on your own? ”

"I borrowed a textbook to read the content of the second semester of my sophomore year, what's wrong?"

"It's only been a few days, and you've already learned the content of the second semester of your sophomore year?"

"Qiao Ze has disrupted the order of knowledge points, according to the rhythm he gave, it is easier to learn."

Chen Yiwen nodded blankly.

So there is still this kind of gameplay?!

"Qiao Ze also said that there is a learning method for doing problems in mathematics, and there is a learning method for research, which is different."

Su Mucheng praised Qiao Zelai for always sparing no effort.

However, as soon as this sentence was finished, it was denied by Qiao Ze: "My original words are that mathematics problems are very important, and you can quickly master and understand what you are learning, but if you want to do mathematical research, you must develop more flexible and open ideas on the basis of doing problems." ”

Su Mucheng stuck out her tongue embarrassedly.

Chen Yiwen looked at Qiao Ze in surprise, this guy didn't raise his head, and even waved his hands quickly on the keyboard of the notebook.

In other words, when he is working hard, he can still hear the conversation between the two word by word, and even give a response.

So is this the kind of legendary genius?

Can you do it with two hearts?

Isn't it true that people don't feel the passage of time and what is happening in the outside world when they are concentrated?

Forget it, don't think about it, let's destroy the earth directly!

……

It was soon time for the library to close.

Chen Yiwen could feel that Qiao Ze was very happy when he finished work, probably because of the progress made in those things that he couldn't understand yet.

He wanted to talk to Qiao Ze on the way back to the dormitory about the difficulties he had learned on his own today.

However......

"Ah, Qiao Ze, let's go around the lake and talk about renting a house tomorrow, okay? By the way, you can also relax your brain. ”

Scold...... Woman!

Are you looking for Qiao Ze to talk about renting a house?!

"Oh, good!"

Hearing this response, Chen Yiwen felt that he had to speak: "That...... What about me? ”

"We can discuss it together."

"Are you alone and afraid to go back to the dormitory?"

Two voices sounded in Chen Yiwen's ears at the same time.

Then he saw Su Mucheng's undisguised warning eyes.

Oh, woman......

"Forget it, I'd better go back first. I suddenly remembered that I had told Lao Gu that I would go back to teach him two questions tonight. ”

Chen Yiwen finally decided not to be a light bulb.

"Oh." Qiao Ze nodded.

……

When Chen Yiwen returned to the bedroom, Zhang Zhou and Gu Zhengliang had already returned to their usual rhythm and were playing.

Seeing Chen Yiwen walk in, Gu Zhengliang, who was probably already resting in the spring, asked casually: "Old Chen, how do you feel about following Brother Qiao to do the project today?" ”

"Group theory is very abstract, and there is something more abstract. Su Mucheng has already begun to learn linear algebra in his sophomore year. Chen Yiwen put the bag on the table and replied lightly.

"What? Sophomore?! Bragging, right? Brother Qiao admitted it, and took Su Mucheng to study on her own for a few days, and she began to soar directly? Zhang Zhou glanced up at Chen Yiwen, a little incredulous.

"Why are you lying to you? Today, the two of them Qiao Ze have already begun to teach Su Mucheng about the problem of dimensionality reduction matrix. Chen Yiwen shrugged his shoulders and looked nonchalant.

"What?! This is a dimensionality reduction strike, right? Outrageous, outrageous! No, Lao Gu, hurry up and call the Education Bureau, someone is illegally opening a cram school in the school. Zhang Zhou said exaggeratedly.

No one paid any attention to him.

After all, this joke is not funny at all.

"I advise you to accept it with peace of mind. There are some things that just feel like soso as long as you accept them! For example, I have fully accepted the fact that I can't compare with those two. ”

As he spoke, Chen Yiwen leaned directly on the chair, put his feet directly on the table, raised his hands to pill his head, and then continued in a relaxed tone

"Anyway, when I see you when I come back, I'm mentally balanced. Follow Qiao Ze to do the project, maybe you can mix a second work after you send a paper in the future, a third work or something, and you can take it out in school to brag about it, maybe there are students who like me who are young and talented? Ay...... Sure enough, people, it is necessary to have comparisons in order to obtain happiness. ”

"Holy!" Gu Zhengliang and Zhang Zhou glanced at each other, and burst out at the same time.

"Lao Chen, you weren't like this before!"

"That's it, are you still the old Chen I know?"

"So learn to grow. Really, you will be grateful to me and Qiao Ze in the future, without me and Qiao Ze, you are still indulging in the fantasy that you are the pride of the sky, but the cruelty of reality lies in the talent...... I won't mention Qiao Ze, you can't compare to those people in Qingbei, right? than the family bottom...... I don't bother to talk about this. I wonder how you can be so good in your mindset? Who gave you the courage to play a game for an hour every night? ”

The Dao Heart collapsed in an instant.

Dormitory 408 finally returned to its normal learning rhythm, and began to be affected by the second person.

This guy's mouth is even more poisonous.

After all, everything Qiao Ze did was unintentional, and Chen Yiwen did it on purpose.

"Aren't we just going to bed and playing two games to find someone to mess with? As for this? Zhang Zhou said with a sad face.

I want to hit someone, but the law and school rules and discipline don't allow it.

"Hey, I'm sorry, but please understand me. I'm a person, once I'm hit, my psychology is easy to be unbalanced, and when my mentality is unbalanced, I feel that nothing is interesting. But now that the blow has shifted to you, I feel like my whole body is full of motivation. So, two brothers, I'm sorry. I'm so refreshed now, I'm going to wash up first. You keep playing, be a man, just be happy, it's okay. ”

After speaking, Chen Yiwen jumped up and walked into the bathroom refreshed.

Only two people were left there looking at each other.

"Damn, I can't stay in this dormitory!" Gu Zhengliang slapped his phone directly on the table and said.

Zhang Zhou nodded approvingly, and said, "Or, let's also apply for a change of bedroom, right?" ”

"Are you really willing?" Gu Zhengliang blinked and looked at Zhang Zhou.

After thinking about it carefully, Zhang Zhou's chubby little face stepped down again: "Forget it, let's work hard to brush the questions, and start quitting the game today!" There will definitely be no chance this year, but next year, if Brother Qiao does a new project, maybe he can pull the two of us along, right? ”

Gu Zhengliang nodded, and then saw that Zhang Zhou had already picked up the exercise book......

Ay......

Roll it!

Roll it up!

……

"You want to rent a room for this project?"

When Li Jiangao received Qiao Ze's call, he was a little surprised.

But on second thought, it's doable.

When the project is in progress, there must be a place for group meetings.

It's really not appropriate to have group meetings in his office all the time.

And in the future, feeding data does need a suitable office space.

"Well, that's a good idea. Who would have thought of it? …… Oh, Su Mucheng, you tell her not to worry, there are many houses to rent in the professor's family area. It's close to the school, so I'll see if I can pick a suitable one. I'll ask you to go and see it when the time comes. ”

"By the way, I have already selected the server plan on my side, and it should be officially signed tomorrow. I'll send you the account and password when the time comes. ”

……

On the edge of the artificial lake not far from the women's dormitory, Qiao Ze hung up the phone and said to Su Mucheng: "Uncle Li also agrees with this idea. But I don't have time tomorrow, I want to get the framework out as soon as possible so that I can get the first batch of data as soon as possible. ”

Su Mucheng said with a smile: "No problem." I've said this a long time ago, I'll do it! Tomorrow I will go to see the house with Uncle Li, and believe me, I will definitely be able to solve this matter. I'm going to help with your research! ”

Qiao Ze nodded, this time he didn't say thank you.

It doesn't feel like it's needed.

However, he corrected the sentence: "It's not just my research, you invested." ”

"Haha, yes, it's our business, so I'm more concerned. I will personally keep an eye on it, and I must decorate this studio that represents our start! Su Mucheng clenched his little fist and raised it fiercely, looking high-spirited.

Qiao Ze nodded and said very scenously: "But the final exam is approaching, and your course can't be pulled down." This year's final exam questions will be difficult, I asked for it. Not to mention that you have to get a perfect score in every course, you should at least be above 90 points in all courses, right? ”

"Huh?!" Su Mucheng was stunned, and asked weakly, "Isn't eighty points good?" ”