I just want to be a quiet scholar

Chapter 7 I'll Just Look, Don't Talk
As a class teacher, Zhang Wanbang was puzzled. Is this still Shen Qi, a scumbag who is addicted to games and has no skills?
As a math teacher, Zhang Wanbang was delighted because his students were discussing Gloria and Weierstrass with him.

The discussion lasted about 10 minutes, basically Zhang Wanbang asked questions and Shen Qi answered.

"We generally think that Cayley is the founder of matrix theory. Cayley has a deduction that the product of two matrices can be zero without one of them being zero, as long as one of them is indeterminate. Shen Qi, you Do you think this inference is correct?"

"Actually, Kayleigh is wrong. This inference is wrong. Both matrices must be indeterminate. I only know the conclusion. If you want me to prove it, Mr. Zhang, my level is limited and I can't do it."

"Weierstrass was the first to get the standard form of bundle A+λB. How do you understand the standard form of this bundle, Shen Qi?"

"A and B here are not necessarily symmetric, but obey the condition that the absolute value of A+λB is not always equal to zero."

"Yes, then its inverse theorem comes from Sylvester and was proved by Weierstrass. If I remember correctly, the advanced textbook of our era wrote a sentence about this inverse theorem, Do you know this sentence?"

"I...I don't know!"

"This inverse theorem says that if the determinant of A+λB is the same as the elementary factor of the determinant of A'+λB', then a pair of linear transformations can be found to change A to A' and B to B' at the same time, Shen Qi said. How do you understand this inverse theorem?"

"I...I don't understand..."

"Gao Dai is indeed too abstract for high school students, but Shen Qi, I am delighted that you can learn this level by yourself."

"Gloria or Weierstrass, matrix algebra or all kinds of determinants, it's hard to explain it to you in a few words." Zhang Wanbang took out a piece of A4 white paper, wrote down a few lines of mathematical symbols, and then handed the white paper to Shen Qi: "Do as much as you can, come to the office this time tomorrow and find me."

Shen Qi took the blank paper and found that there were five math problems written on it. It seemed that Teacher Zhang wanted to test himself further.

"Okay, see you tomorrow, Teacher Zhang." Shen Qi said goodbye to Zhang Wanbang and left the teacher's office.

Back in the classroom of Class 2 of Senior Two, Shen Qi began to tackle the exam questions given by Zhang Wanbang.

The first question is to prove the Cauchy-Schwartz inequality: XXXXXX (a mathematical formula that cannot be displayed by a mobile phone), and give the conditions for the establishment of the equal sign.

This question is not too difficult. The entry-level proof questions of "Advanced Algebra" test the concept of inner product space.

Shen Qi quickly completed the proof and wrote the proof process on white paper.

System: "The host successfully solves the problem, and will be rewarded with 2 points for the master."

"Hehe, 2 points for Xueba." Shen Qi can't get Xueba points for doing high school math problems now, but he can get Xueba points for doing college math problems.

At the same time, the Chinese teacher walked into the classroom. This is a Chinese class.

Shen Qi focused on solving Zhang Wanbang's math problems. He didn't listen carefully to the Chinese class. After all, people's energy is limited and it is difficult to do two things.

The second problem proposed by Zhang Wanbang is to solve a system of linear equations, which requires the combined use of Gaussian elimination and the properties of augmented matrices, which increases the difficulty.

Shen Qi encountered some obstacles in the process of solving the problem. Implementing elementary transformation on the linear equation system is equivalent to implementing row transformation on its augmented matrix.

system of equations → augmented matrix
Augmented matrix → system of equations
Eliminate the x1 term in the first equation

Then the third row of the augmented matrix is ​​transformed
Add 4 times the second equation to the third equation, and eliminate the x2 term in the third equation to get a ladder-shaped system of equations

Then the augmented matrix should also be transformed into...

"My eyes are so beautiful..." Shen Qi switched back and forth between the linear equation system and its corresponding augmented matrix, until he doubted life.

Shen Qi bit the bullet and forcibly solved the problem. The process was very painful, but he gritted his teeth and passed this hurdle, and the reward was double the pleasure.

After spending an entire Chinese class and burning countless brain cells to death, Shen Qi finally solved the second question posed by Zhang Wanbang.

"The host solves the problem successfully and will be rewarded with 5 scholar points."

Originally, the Chinese class could get 1 Xueba point, but Shen Qi didn't listen carefully, so the contribution of this Chinese class to Xueba's points was 0.

In fact, it doesn't matter anymore, because Shen Qi solved two math problems in the Chinese class and earned 7 points for the top student.

"Doing two math problems is equivalent to taking seven Chinese classes and doing 200 math problems for college students... Forget it, take a break first." During the break, Shen Qi took out "Advanced Algebra" from his schoolbag and reviewed it. Specialized courses for undergraduates in mathematics.

First-year students of the Department of Mathematics have three compulsory basic courses, namely "Advanced Algebra", "Mathematical Analysis" and "Analytical Geometry".

Among them, the simplest solution is the solution, which can be understood as a three-dimensional version of high school plane analytic geometry.

In terms of abstraction, the most difficult is the high generation.From a computational point of view, the most difficult part is the score.

As for the follow-up real variable functions, functional analysis, topology, partial differential equations, differential geometry, algebraic geometry and other branches, whoever has the ability will study it, and whoever has no ability will fail the course.

"Hey, Shen Qi, what book are you reading?" Chen Xiaoting noticed that Shen Qi was reading a strange book.

"High Generation." Shen Qi closed "Higher Algebra" and pushed it to Chen Xiaoting's desk.

Chen Xiaoting was dumbfounded when she saw the cover: "Advanced algebra, a full-time college mathematics textbook, this...is this a college student's textbook?"

"Yes." Shen Qi nodded.

"I'll just take a look, don't talk." Chen Xiaoting turned a few pages symbolically, and then returned "Advanced Algebra" to Shen Qi: "Could it be that your perfect score is this "Advanced Algebra"?"

"No, this book doesn't directly help improve high school math scores."

"Then why are you studying it?"

"What Gao Dai provides is a kind of abstract thinking logic. If you say it is useful, it is very useful. If you say it is useless, it is worthless." In the face of incomparably huge mathematics, Shen Qi is still an apprentice. The ultimate meaning of mathematics What it was, Shen Qi couldn't tell, he explored it in his own way.

"It looks very profound, but it has nothing to do with me. I only got 85 points in the math test this time. I really regret being assigned to the science class." Maintain the overall score ranking in the middle grade.

At this time, the school radio began to play the athletes' march, and it was time for the recess.

"Let's go, let's do the exercises." Shen Qi got up and greeted Chen Xiaoting to go downstairs together.

Chen Xiaoting covered her lower abdomen and smiled awkwardly: "I'm not feeling well, I won't do exercises today."

Oh, auntie is here, it really can't be done, jumping and jumping is easy to happen.Shen Qi has heard all kinds of rumors about the aunt, and the current high school students know everything: "Then you have a good rest and tell me what you need."

"Actually, it's not a big problem, you can go do the exercise." Chen Xiaoting blushed, how dare you tell you guys about the needs of girls?
Within minutes, thousands of students had assembled on the school's large playground, lined up by class.

Nangang No. [-] Middle School has a long history. It was established by patriotic revolutionaries during the Republic of China. The principal strictly implements the basic policy of "strengthening the body, developing in a balanced way, teaching without distinction, and treating students equally". social commitment.

After the ninth set of radio gymnastics ended, Shen Qi stayed on the playground, followed by physical education class.

For most boys, physical education class is the happiest time, and it is a rare adjustment after heavy studies.

The principal of Nangang No. [-] Middle School fulfilled the promise of "strengthening the body and developing in a balanced way", and the physical education class will be retained until the third year of senior high school.

(End of this chapter)