From Almighty Scholar to Chief Scientist

Chapter 40 I'll Give You Some Questions

There are eight days of intensive training courses after the exam.

At the beginning, Lin Xiao still went to class seriously. Of course, it’s another matter if he took the class seriously, but later found that many training team members didn’t go to learn. Basically, only the students who signed up with their own money would attend the class. He didn't go to class after three days.

Of course, the self-study room is also open for the training camp. You can go to the self-study room to study every day. There is also a math teacher there. If you encounter problems during self-study, you can ask the teacher.

However, Lin Xiao was just reading and had nothing to ask, so he just stayed in the study room to enjoy the quiet study atmosphere.

It's just that he didn't look for the teacher, but the teacher walked around the study room and finally found him.

The teacher in charge of the self-study room is Xu Hongbing, a professor of mathematics.

He walked to Lin Xiao's side and glanced at this boy who was called the genius of the geniuses of mathematics geniuses.

This student is quite famous in their training team, so it is normal for him to know Lin Xiao, but this student...is actually reading abstract algebra?
Abstract algebra is not easy. Although he doesn't teach it in school, it doesn't prevent him from knowing that the failure rate of abstract algebra has always been high, because most of the students who fail in advanced algebra will also pass abstract algebra.

"Do you understand?"

"Ah?" Lin Xiao recovered from the state of immersion, and then saw the teacher standing next to him, and called out: "Teacher Xu."

Then he replied: "It's okay, I can understand it."

"Gao Dai, have you read it?"

"finish watching."

"Sure." Xu Hongbing nodded approvingly. Such a mathematical genius is truly not wasting his talent.

If Lin Xiaohui forgets to make progress because he is invincible in the math competition now, then obviously he will not have too high achievements in the future.

Only by constantly learning and making progress can the talent of a genius be brought into full play, otherwise, it will obviously end up like Hu Zhongyong.

At this moment, Xu Hongbing thought for a while and said, "Then I'll give you a question, and you do the math."

Lin Xiao nodded: "Being respectful is worse than obeying orders."

"Your boy is still very polite."

Xu Hongbing joked with a smile, then took Lin Xiao's pen and began to write questions on his draft paper.

Although he does not teach abstract algebra, Gao Dai still taught it, and it is quite simple to come up with a question.

[Assume that the square matrix F of order n is a friend matrix of a certain polynomial, and prove that the square matrix interchangeable with F can only be a polynomial of F. 】

"bring it on."

After finishing writing, Xu Hongbing handed over the pen to Lin Xiao.

The question he asked was quite difficult. He also wanted to test how well Lin Xiao had learned Gao Dai, and whether he could reproduce the performance of blocking and killing gods and Buddhas in the Olympiad exam.

In addition, there is also a knowledge point, that is, the friendship matrix. He wants to know how well Lin Xiao grasps this remote knowledge point, or whether the knowledge is extensive.

But to his surprise, Lin Xiao just started writing after thinking for a minute, without asking him what the friend matrix is.

[Proof: Suppose V is an n-dimensional linear space, ε1, ε2, ..., εn are a set of basis.Let ψ be the linear transformation of V, so that the matrix of ψ under the basis ε1, ε2, ..., εn is F, that is, ψ(ε1, ε2, ..., εn)=(ε1, ε2, ..., εn)F.

Because F is a friend matrix, so ε2=ψ(ε1), ε3=ψ(ε1),…, εn=ψ^(n-1)(ε1). That is…]

Seeing Lin Xiao's two operations in front of him, Xu Hongbing took a deep breath. Can he use linear space and linear transformation so proficiently?
Even in advanced algebra, this knowledge is also a difficult point. He used to be cautious when asking such questions, for fear of confusing the students.

Moreover, he didn't expect Lin Xiao to think of using this method to solve it so quickly. Generally speaking, students basically use standard unit column vectors to solve it.

He couldn't help feeling in his heart, this student is really amazing.

No wonder being able to show such momentum in the Olympiad, this is simply born for mathematics.

With waves in his heart, he just looked at Lin Xiao to write like this.

It didn't take long for Lin Xiao to write to the last step.

【所以C=（n∑i=1）ci1*F^(i-1)(e1，Fe1，Fe1，…， F^(n-1)e1)=(n∑i=1)c1F^i-1
So C is a polynomial in F.

Certificate completed. 】

After writing the last two characters stroke by stroke, Lin Xiao put down the pen.

Seeing that he finished writing, Xu Hongbing said, "Very good, you did a good job."

Lin Xiao smiled and said, "Actually, it's not too difficult, it's nothing."

Xu Hongbing: "..."

"You don't think it's too difficult?"

Lin Xiao nodded, and said truthfully: "It's really okay. I actually just finished reading advanced algebra a few days ago. If I can do it, it shouldn't be too difficult, right?"

Xu Hongbing: "..."

He felt the contempt from the student in front of him for the question he posed.

Moreover, Lin Xiao actually said that he had only finished reading advanced algebra for a few days?

"You just read the high math?"

"Yes."

"Self-study?"

"Self-taught."

"No teacher to guide you?"

"No." Lin Xiao said: "I don't have this kind of college mathematics tutoring in my hometown. Before I participated in the Olympiad, I didn't participate in any training. Oh, that is, before the mathematics league, our school held a month of mathematics league training. class."

Hearing Lin Xiao's words, Xu Hongbing felt even more unbelievable. Lin Xiao is still self-taught?
He originally thought that Lin Xiao was able to do it because of his teacher and his own talent.

Perhaps the teachers of mathematical geniuses have little contribution to their achievements, but mathematical geniuses must have a teacher's guidance.

Newton was so powerful, his teacher was the 'Professor Lucas' of Cambridge University at that time. Professor Lucas did not refer to a certain person, but an honorary position. Only recognized scholars can obtain this position, and at the same time only Being held by a teacher is enough to show how powerful Newton's teacher is.

Besides, Einstein's teacher is Minkowski. The famous Minkowski space-time has a very important position in the field of mathematical physics, and it has a very close relationship with Einstein's later theory of relativity.

Therefore, Xu Hongbing found it incredible.

Lin Xiao lived in such a lack of educational environment, but he still showed such a strong mathematical talent.

Sure enough, gold always shines. At the same time, he couldn't help but feel sorry for Lin Xiao. If he could have a good teacher to guide him, Lin Xiao would have soared into the sky long ago, right?
For example, I joined the IMO team when I was in junior high school.

But soon, he thought that Lin Xiao would be entering university soon, and as expected, Lin Xiao would choose those two schools.

In this way, he doesn't have to worry about Lin Xiao's future. Such a genius will never be ignored in college.

Of course, the above are all the attitudes that he, as a teacher, maintains towards any student and wants him to be good. Leaving aside these things, the questions he asked were underestimated. How can this be tolerated?

Can he be wronged? As a professional mathematics proposition person.

He was invited to participate in the CMO and the proposition group of the college mathematics competition, which is why he was invited to tutor these students.

So he said: "Then you are self-taught, very good, very good, I believe that after you go to university, you will be able to achieve better growth."

"How about this, I will give you a few more difficult questions later, and when you plan to leave later, I will come to the podium to take them."

"Ok."

Lin Xiao nodded.

　Thanks to the book friend Fleeting Time_Passing Water for the 500 starting point reward, and thanks to the book friend Extrem, Xiaoshuai Shuxing Xingxing, Jiafei Mao who loves snacks, and 20170728194229879 for the 100 starting point reward.

　　Thank you for your support
　　
　
(End of this chapter)