I Just Want to Be a Quiet Top Student

　　As a class teacher, Zhang Wanbang is puzzled. Is this still Shen Qi, a silly student who is addicted to games and has no skills?

　　 As a math teacher, Zhang Wanbang is delighted because his students are discussing Gloria and Weilstrass with him.

　　 This discussion lasted about ten minutes, basically Zhang Wanbang asked questions and Shen Qi answered.

"We generally believe that Gloria is the founder of matrix theory. Gloria has an inference 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?"

　　 "In fact, Gloria was wrong. This inference is wrong. Both matrices must be indefinite. I only know the conclusion. If you want me to prove it, Mr. Zhang, my level is limited."

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

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

"Yes, then its inverse theorem came from Sylvester and was proved by Weilstrass. If I remember correctly, the high-generation textbooks of our time 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 consistent with the elementary factors of the determinant of A'+λB', then a pair of linear transformations can be found at the same time to change A to A'and B to B', Shen Qi How do you understand this inverse theorem?"

　　 "I...I can't understand..."

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

"Gloria or Weilstrass, matrix algebra or all kinds of determinants, it's hard to tell you clearly 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 it. Shen Qi: "As much as you can do, come to the office to find me at this time tomorrow."

　　 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.

　　 Returning to the classroom in Class 2 of high school, Shen Qi began to conquer Zhang Wanbang’s exam questions.

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

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

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

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

　　 "Oh, 2 points for academic mastery." Shen Qi can't get academic master points for doing high school math problems, but he can get academic master points for college math problems.

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

　　 Shen Qi had no other intention to solve Zhang Wanbang's math problems. He did not listen to the Chinese class carefully. After all, the energy of human beings is limited and it is difficult to do two tasks.

　　 Zhang Wanbang’s second question is to solve a linear equation system, which requires a comprehensive use of the Gaussian elimination method and the properties of augmented matrices, which increases the difficulty.

　　 Shen Qi encountered some obstacles in the process of solving the problem. The elementary transformation of the linear equations is equivalent to the transformation of the rows of the augmented matrix.

　　 equations → augmented matrix

　　 augmented matrix→equation system

　　 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, eliminate the x2 term in the third equation, and get a ladder-shaped equation system

　　 Then the augmented matrix has to be transformed into...

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

　　 Shen Qi bit his scalp and forcibly solved the problem. The process was very painful, but after gritted his teeth, the gain was doubled pleasure.

　　 spent a whole Chinese class time, burned countless brain cells, Shen Qi finally solved Zhang Wanbang's second question.

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

　　 The original Chinese class can get 1 point of Xueba points, but Shen Qi did not listen carefully, so the contribution of this Chinese class to Xueba points is 0.

　　 Actually, it doesn’t matter, because Shen Qi solved two math problems in the Chinese class and gained 7 points for learning tyrants.

"Doing two math problems is equivalent to taking seven Chinese classes and 200 math problems for college students... Forget it, let's take a break." During the break, Shen Qi took out "Advanced Algebra" from his schoolbag and revisited mathematics. Department of professional courses for college students.

　　 Mathematics freshman has three compulsory basic courses, which are "Advanced Algebra", "Mathematical Analysis" and "Analytic Geometry".

　　 Relatively speaking, the simplest is the solution, which can be understood as a three-dimensional version of high school plane analytical geometry.

　　 In terms of abstraction, the most difficult thing is high generation. In terms of the amount of calculation, the most difficult thing is to count the points.

　　 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 to study it, whoever does not have the ability to fail.

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

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

　　 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?"

　　 "That's right." Shen Qi nodded.

　　 "I'll just take a look, and don't speak." Chen Xiaoting turned a few pages symbolically, and then returned "Advanced Algebra" to Shen Qi: "Is this "Advanced Algebra" your secret book of perfect scores?"

　　 "No, this book does not directly help improve high school math scores."

　　 "Then why are you studying it?"

"What Gaodai provides is a kind of abstract thinking logic. Say it is useful. It is useful. Say it is useless. It is worthless." In the face of immense mathematics, Shen Qi is still an apprentice, UU reading www. What is the ultimate meaning of uukanshu.com's mathematics? Shen Qi also didn't know clearly. He explored in his own way of understanding.

"It looks so esoteric, but it has nothing to do with me. I only scored 85 points in the math test. I really regret being assigned to the science class." Chen Xiaoting's mathematics, physics and chemistry results are very average. She relies on Chinese and English to get points. Maintain the overall score ranking in the middle class.

　　 At this time, the school radio began to broadcast the athletes’ march, and it was time for exercises between classes.

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

　　 Chen Xiaoting clutched her lower abdomen and smiled awkwardly: "I don't feel well, so I won't do exercises today."

　　 Oh, my aunt is here, so I really can’t do exercises, it’s easy to jump around. Shen Qi has heard all kinds of rumors about her aunt, and the current high school students know everything: "Then you have a good rest and tell me what you need."

　　 "In fact, it doesn't matter, you go and do exercises." Chen Xiaoting's blush, how embarrassed to tell you boys about the needs of girls?

　　 Within a few minutes, thousands of students gathered on the school’s playground, and they lined up in class.

Nangang No. 2 Middle School has a long history and was founded by patriotic revolutionaries during the Republic of China. The principal strictly implements the basic policy of "strong physical fitness, balanced development, education without discrimination, and equal treatment". The promise of society.

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

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

　　 The principal of Nangang No. 2 Middle School has fulfilled the promise of "strengthening physique and balanced development". The physical education class will be retained until the third year of high school. In some high schools, the physical education class was abolished in the second year of high school.