From all-round academic master to chief scientist

The little brother refused, and without saying much, Lin Xiao took out the book "Real Variable Functions and Functional Analysis" he was reading from the satchel he had 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 has also come to the functional analysis part. Functional analysis is even more heavyweight. It has already involved analytical problems in infinite-dimensional vector spaces. The difficulty is so difficult that there is no need to worry about it. Say more.

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

But when the little brother next to him saw that the big brother next to him actually pulled out a book and started reading it, he couldn't help but become curious.

What book was he reading?

The little brother glanced out of the corner of his eye, real variable function and functional analysis?

Suddenly I felt confused.

It looks pretty cool.

Also, functions?

Is this a math book?

Seeing that Lin Xiao didn't notice him, he quietly turned his head and took a look. He suddenly felt dazzled. Is this considered mathematics?

Are there so many weird symbols in mathematics?

But the little brother was just surprised for a while, and then thought that he just didn't learn those things. If he had learned as much as Lin Xiao, 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 you learn mathematics in high school, you will definitely understand it.

So the little brother stopped looking at it and continued to work on his own questions.

He went through one question after another. When he was doing a big geometry question, he finally encountered something he couldn't figure out.

"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 was an isosceles triangle.

However, at this time, he remembered that there was a great figure next to him who was praised by his parents every day. He couldn't help but turn his head and look at Lin Xiao. This guy was still reading the book about unknown functions, and his eyes murmured. After a while, I came up with the idea of ​​trying Lin Xiao.

So he said: "Hey, please help me look at 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 reading stupidly.

"Hello? Hello?!"

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

Although he was talking to his little brother, Lin Xiao was still thinking about the Hahn-Banach theorem in the book.

"I've come across a question here. See if you can write it out." The little brother pointed to the question he was writing.

"Oh, are you having a problem? Let me take a look."

Lin Xiao leaned over and took a look at the question. It was a triangle plus a circumscribed circle, and there were some line segments inside the triangle. The corresponding conditions were given, and then he asked if the triangle AHD was an isosceles triangle.

But Lin Xiao, whose mind was filled with the Hahn-Banach theorem, couldn't help but start thinking about the Hahn-Banach theorem.

At this time, the little brother next to him added: "If you can write it within three minutes, I will consider you great."

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

If he couldn't write his junior high school question in three minutes, he would never approve it.

However, Lin Xiao didn't listen at all to what he said. At this time, he had completely transformed the 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 writing and talking about the process, because he still remembered that he was coaching others.

"We first convert the Euclidean space where the plane is located into Banach space, and let it be X, because Banach space is a completely normed vector space, that is, it has a 'length'."

When the little brother heard Lin Xiao's words, he was immediately confused. You Sousa?

What Euclidean space, what Banach space?

What is a completely normed vector space?

But it was 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 Letter f satisfies the following conditions..."

As he said this, Lin Xiao also wrote on the paper:

[(1) f(x)= f0(x) (for any x ∈ X0);

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

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 the function f(x)=..." based on the circle and triangle where they are located.

…

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

Are you kidding me?

What the hell kind of talismans are these?

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

In this way, he watched Lin Xiao's writing becoming more and more 'scary'. He could understand every word, but when they were connected together, he was just confused or confused?

But this person thought he could keep up with the rhythm, talking and writing at the same time, without caring about his feelings at all.

till the end--

“So we can know that if the function

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

[Certificate completed].

After writing the last two words one by one, Lin Xiao nodded with satisfaction. As expected of himself, the knowledge he had just learned could be used to solve problems.

"Do you understand?"

At this time, Lin Xiao remembered that he seemed to be tutoring someone. After asking a question, he looked at his little brother.

As a result, he saw his little brother looking at him blankly, thinking about the three ultimate questions of philosophy.

Lin Xiao suddenly realized, why did he use functional analysis to solve this problem?

This is a junior high school geometry question!

"Uh, sorry about that, I made a mistake, try again."

Lin Xiao quickly went back and read the question again, and immediately said: "This question is very simple. First make auxiliary lines, connect BH, BD, DC, and then connect the four points A, B, C, D and O. Get up, and then you..."

Once the auxiliary lines are made, it will be easier to solve.

"Look, didn't we just prove that the two sides are equal? ​​The problem is solved. It's quite simple."

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

He waved his hand in front of his little brother and shouted, "Zhou Mingyu?"

"Wow!"

As a result, the next moment, the little brother broke down because of Lin Xiaoxiu and burst into tears, which shocked Lin Xiao.

"Hey, why are you crying?"

Are these twelve-year-olds so fragile?

The door was opened, and several elders heard the crying and came in, but they saw that the two brothers were not fighting.

Mom Yang Rong thought Lin Xiao was bullying others, but thinking about Lin Xiao's usual behavior, it didn't look like she would bully others, so she asked, "What's going on?"

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

Alas, it is so difficult for children nowadays to understand.

Thanks to Gu Wendao for the 5,000 starting coin reward, thank you to Gong Changchang Long Chang Chang Chang Chang Chang Chang Ah Ah for the 1,500 starting coin reward, thank you to Silently Reading for the 1,000 starting coin reward, thank chaunce and I Love Magic for the 500 starting coin reward. Rewards, thank you for the 100 starting coin rewards for Where Are the People Who Want to Fly, Dapeng Goes to Ninety Thousand Miles, Silent M, Dupont Line, and Lonely Rising.

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