From Almighty Scholar to Chief Scientist

Chapter 58
The little brother refused, Lin Xiao didn't say much, and took out the "Real Variable Function and Functional Analysis" he was reading now from the satchel he brought.

Real variable functions and functional analysis are as difficult as complex variable functions, and Lin Xiao has to be serious enough to learn them.

Now that he has finished reading the previous part on real variable functions, he also came to the part of functional analysis. Functional analysis is even more heavyweight. It has already involved the analytical problems in infinite-dimensional vector spaces. The difficulty is difficult, so it is naturally unnecessary. Say more.

So after a while, he fell into the state of immersion again.

But when the little brother next to him saw that the big brother next to him had turned out a book and read it, he couldn't help but become curious.

What book did he read?

The little brother glanced at it from the corner of his eye, real variable function and functional analysis?
Immediately I didn't know what was going on.

It looks like it's awesome.

Also, functions?
Is this a math book?

Seeing that Lin Xiao didn't notice his appearance, he quietly turned his head and glanced at it, feeling dazzled immediately. Is this counted as mathematics?

There are so many strange symbols in mathematics?

But the little brother was only surprised for a while, and then he thought that it was just that he hadn't learned those things. If he had learned Lin Xiao's level, he would definitely be able to understand this book, just like he didn't study in high school now. Mathematics knowledge, but as long as I have learned mathematics in high school, I will definitely understand it.

So the little brother stopped reading more and continued to work on his own questions.

After doing one problem after another, my little brother finally encountered something that he couldn't think of when he was doing a big geometry problem.

"This question is a bit difficult."

He wrinkled his face and thought about it, but he couldn't figure out how to prove that this triangle is an isosceles triangle.

However, at this time, he remembered that there was a god-level person beside him who was praised by his parents every day. He couldn't help but turned his head to look at Lin Xiao. Turning around, the idea of ​​trying Lin Xiao came up.

So he said, "Hey, help me see this question and how to write it."

However, Lin Xiao did not respond.

The little brother couldn't help but wonder if Lin Xiao was stupid from reading.

"Hello? Hello?!"

He stretched out his hand and shook it in front of Lin Xiao. At this moment, Lin Xiao finally came back to his senses, looked at him suspiciously, and asked, "What's the matter?"

Although he was talking with his younger brother, Lin Xiao still recalled the Hahn-Banach theorem in the book in his mind.

"I've come across a question, see if you can write it down." The little brother pointed to the question he was writing.

"Oh, have you encountered a problem? Let me take a look."

Lin Xiao turned his head and glanced at the question. A triangle plus a circumscribed circle, and some line segments inside the triangle, and gave the corresponding conditions, and then asked whether the triangle AHD is an isosceles triangle.

But Lin Xiao, whose mind is full of the Hahn-Banach theorem, can't help but start thinking from the Hahn-Banach theorem at this time.

At this time, the little brother next to him added another sentence: "If you can write it in 3 minutes, I will count you as good."

He wanted to see how good at mathematics this person his parents talked about every day was.

If he can't write his junior high school question in 3 minutes, then he will never agree.

However, Lin Xiao didn't listen to what he said at all. At this time, he had completely transformed this problem into the vector space in functional analysis.

He took out the draft paper next to him and started writing directly.

At the same time, he was talking about the process while writing, because he still remembered that he was tutoring others.

"We first convert the Euclidean space where the plane is located into Banach space, and set it as X, because Banach space is a fully normed vector space, that is, its existence 'length'."

The little brother was stunned when he heard Lin Xiao's words, you Sousa?

What Euclidean space, what Banach space?

What is a fully normed vector space?

But it’s not over yet, Lin Xiao continued: “According to Banach’s theorem, if X0 is a subspace of X, then f0 is a bounded linear functional defined on X0, then there must be a bounded linear functional on X. The function f satisfies the following conditions..."

As he spoke, Lin Xiao also wrote on the paper:

[(1) f(x)= f0(x) (for any x ∈ X0 );

(2) || f ||=|| f0 || (below table 0).

Then || f0 || (Table 0 below) represents the norm of f0 on X0. 】

"Then convert point A, point B, point C... into points in this space, and construct function f(x)=..."

……

Looking at what Lin Xiao wrote, the little brother was even more confused.

are you kidding me

What the hell are these?

This is just a junior high school question, okay? !

In this way, he watched Lin Xiao's writing become more and more 'scary', he could understand every word, but when they were linked together, he was at a loss besides at a loss?
But this person thought he could keep up with the rhythm, and wrote while talking, without caring about his feelings at all.

till the end--

"So we can know that the function X of the triangle is a linear functional on Y, then all operators are equal, so we can easily know the norm ||T||1=||T||2."

"Because it is a linear operator, it returns to the Euclidean space, that is, AH=HD, that is, the triangle AHD is an isosceles triangle."

【Certificate completed】.

After writing the last two words stroke by stroke, Lin Xiao nodded in satisfaction. As expected of him, the knowledge he just learned can be used to solve problems.

"Do you understand?"

At this time, Lin Xiao remembered that he seemed to be tutoring others, so he couldn't help asking, and then looked at the little brother.

In the end, I saw my little brother staring blankly at himself, thinking about the three ultimate questions of philosophy.

Lin Xiao suddenly came to his senses, why did he use functional analysis to solve this problem?
This is a junior high school geometry problem!
"Uh, sorry about that, I made a mistake, try again."

Lin Xiao hurriedly looked back at the question again, and immediately said: "This question is very simple, first make an auxiliary line, connect BH, BD, DC, and then connect A, B, C, D to point O Get up, and then you..."

Once the auxiliary line is made, it will be easier to solve it.

"Look, didn't we prove that the two sides are equal, the problem is solved, it's quite simple."

After Lin Xiao finished writing, he turned his head to look at the little brother, but he still looked dumbfounded.

He stretched out his hand and shook it in front of his little brother, and shouted, "Zhou Mingyu?"

"Wow!"

As a result, the next moment, the little brother burst into tears because of Lin Xiaoxiu's collapse, which shocked Lin Xiao.

"Hey, why are you crying?"

Are all 12-year-olds this vulnerable?

The door was opened, and several elders heard the crying and walked in, but saw that the two brothers did not fight.

Mother Yang Rong thought that Lin Xiao was bullying others, but thinking of Lin Xiao's usual performance, she didn't seem to be able to bully others, so she asked, "What's going on?"

Lin Xiao spread his hands innocently and said, "How do I know, I just helped him write a question, okay?"

Alas, today's children are really hard to understand.

　Thanks to Gu Wendao for the reward of 5000 starting coins, thank you for the reward of 1500 starting coins, thank you for the reward of 1000 starting coins for reading silently, and thank you for chaunce, I love magic for the 500 starting coins Rewards, thank you for the 100 starting point rewards of where is the person who wants to fly, Dapeng goes straight to [-] miles, Mom, Dupont Line, and Lonely Rising.

　　Thank you for your support!

　　
　
(End of this chapter)