Xueba starts with change

Chapter 559 This gust of wind is really timely...

In fact, it is not correct to say that it is new mathematics.

Because that's what basic math is about.

is about solving for eigenvectors.

Eigenvectors and eigenvalues ​​refer to multiplying a matrix by a vector, which is equivalent to doing a linear transformation.

But the direction of this vector will often change.

But if there is a matrix A, let the direction of this vector v remain unchanged after linear transformation, but only stretched or compressed by a certain multiple.

That is, Av=λv.

Then, this vector v is the eigenvector, and λ is the eigenvalue.

The traditional solution here is to start from the calculation of the characteristic polynomial, then solve the eigenvalues, then solve the homogeneous linear equations, and finally obtain the eigenvectors.

That's right, the content of this part, in the eyes of mathematicians, is nothing more than ordinary, basic mathematical solution formulas.

However, Chen Zhou discovered it when calculating the probability of neutrino oscillation.

The geometric nature of eigenvectors and eigenvalues ​​is actually the rotation and scaling of space vectors.

And the three flavors of neutrinos, that is, electron, muon and tauon, aren't they equivalent to the transformation among three vectors in space?
Therefore, when studying neutrino oscillation related topics, Chen Zhou accidentally discovered that there is a more general law between eigenvectors and eigenvalues.

Thus, a new and wonderful solution appeared in Chen Zhou's mind.

"If you know the eigenvalues, you only need to write a simple equation, and the eigenvectors can be solved..."

Chen Zhou, who was thinking this way, kept writing on the draft paper with the pen in his hand, and began to describe the new formula in his mind.

Converting physical problems into mathematical problems has always been Chen Zhou's habitual research method.

And once the physical problem can be converted into a mathematical problem, then for Chen Zhou, it will no longer be a problem.

Although there is still a long way to go to solve the problems related to neutrino oscillation.

However, this new discovery still made Chen Zhou full of interest.

"Create a submatrix by deleting the rows and columns of the original matrix..."

"The eigenvalues ​​of the submatrix and the original matrix are combined to calculate the eigenvectors of the original matrix..."

"You can also get ∣^Uαi∣=(λi-ξα)(λi-Xα)/(λi-λj)(λi-λk)..."

Chen Zhou stopped writing slowly, looking at the content on the draft paper.

The new formula has been found by him, and there is only a proof process left.

If the proof process...

Chen Zhou took out a new draft paper again, and clenched the pen in his hand.

The proof begins.

"First define A as an nxn Hermitian matrix with eigenvalues ​​λi(A) and normed eigenvectors vi..."

"Each element in the eigenvector is labeled vi, j..."

"By deleting the jth row and jth column, the submatrix Mj of A can be obtained, the size is (n-1)×(n-1), and its eigenvalue is λk(Mj)..."

"Then, by proving that a Cauchy-Binet type formula can be obtained..."

"Again, it can be proved by Lemma 1 and Lemma 2..."

"...by the definition of conjugation, the diagonal elements on the left side of Equation 7 determine the submatrix of λi(A)In-A..."

"...Therefore, applying Lemma 2, the corollary is that if an element in the eigenvector disappears, vi,j=0, then the eigenvector equation of matrix A will be reduced to an eigenvector equation of its submatrix Mj .”

Chen Zhou's thinking is very clear, and the whole proof process is also very smooth.

Without encountering the slightest obstacle, this new formula was proved.

"It's interesting. After such a long time, no one has discovered this?"

Chen Zhou looked at the proof process on the draft paper in front of him, with a strange smile on his face.

If anything, the new formula is not complicated.

As for the proof methods of the new formula, Chen Zhou was able to give at least five methods.

But it is such an uncomplicated new formula and proof process, why has no one discovered it for so long?

Chen Zhou was a little puzzled, but also a little lucky.

This shows that it has to be him!
Without him, who knows how long this formula will have to be silent before it can be seen with the world?
This is not Chen Zhou's narcissism, but the value of this new formula, which is indeed quite large.

Whether it is mathematics, physics, or engineering, it has very practical significance.

In these disciplines, there are still many problems that involve the calculation of eigenvectors and eigenvalues.

For example, Chen Zhou discovered the source of this new formula, the calculation of neutrino oscillation probability.

For another example, in the field of machine learning, data dimensionality reduction and face recognition also involve the practical application of matrix eigenvalue and eigenvector theory.

Think about it, in any case, you don't need to know any elements in the matrix, you can calculate anything you want, isn't it awesome enough?

Of course, Chen Zhou didn't think too much about it, nor did he think about the possible impact of this new formula.

Chen Zhou didn't intend to sort out the relevant content of this new formula immediately, and then publish it in a journal.

He just thinks that this thing is still easy to use.

At least, it saved him a lot of work in the calculation of neutrino oscillation probability.

If you want to organize it into a paper and submit it, how can you get it? You have to wait for him to solve the neutrino oscillation related topics.

Satisfied, Chen Zhou tidied up this "accidentally discovered" new formula and its proof process, and put it aside.

Then, he raised his hand and looked at his watch. It was almost noon.

After thinking about it, Chen Zhou did not continue the research on neutrino oscillation related topics, but chose to settle lunch first.

Since the timing of proving the new formula happened to be so precise, there was no need to forcefully delay the time.

In the afternoon, it is time to belong to the minimal model program.

The rotation of physics topics and mathematics topics.

As for the time to research and prove new formulas, whether it belongs to mathematics or physics.

Chen Zhou felt that it should be attributed to physics.

After all, the most direct and effective effect of the discovery of the new formula is the research on neutrino oscillation related topics.

It should be known that the calculation problem of neutrino oscillation probability is the core issue of neutrino oscillation related subjects.

So the time spent on researching new formulas and proving new formulas should not be counted as a physics subject?

Sitting in front of the desk again, Chen Zhou found a few draft papers from another pile and looked at them carefully.

That's right, on Chen Zhou's desk, there are two piles of draft paper corresponding to the topics of the two subjects.

This is just the "research manuscript" he completed after retreating.

The previous piles of draft paper were all placed under the desk by him.

Otherwise, the desk would have been full.

Time was passing by slowly, but Chen Zhou was always looking at the draft paper in his hand.

In his mind, he kept reviewing and summarizing the research content of the past few days.

The second problem of the minimal model program is not as easy to solve as he expected.

The original inspiration brought by Xu Chenyang, as well as the thought that he thought to be stable, seemed to have entered a new fork.

Chen Zhou encountered new troubles in the research of the minimal model program.

"It is necessary to ensure the uniqueness of the extremely small model, but in fact, it is very likely that it is not unique..."

Putting down the draft paper in his hand, Chen Zhou frowned and thought.

The Chen Zhou at this time was completely different from the high-spirited him in the morning.

In the morning, he seemed to be a controller, holding everything in his hands.

But now he is like a seeker, unable to figure out where the direction is.

Suddenly, Chen Zhou reached out and took out a new stack of A4 draft paper.

He unscrewed the cap of the pen and began to bury his head in the draft paper.

He intends to take a new attitude and re-study the entire minimal model program.

Since you don't know where the direction is, let's go all over again!

Chen Zhou, who was thinking like this, quickly left clear handwriting on the draft paper.

Of course, Chen Zhou didn't start all over again.

He is to clarify the original direction.

To put it simply, it is to clarify the ideas brought by inspiration.

Therefore, although Chen Zhou was writing the content of the research quickly on the draft paper.

But these contents, compared with before, have also been much less.

Most of the thinking and calculation process were completed in Chen Zhou's mind.

Unlike before, Chen Zhou began to grasp more details.

Whether it is his own research process or the literature he combed.

Chen Zhou didn't let any of them go.

He re-filtered all the content, all the details, in his mind.

"I remember that there is a literature that simplifies the calculations in the original proof by introducing some concepts. This is also the application of the results of some singular varieties studied by algebraic geometers in recent years..."

Chen Zhou recalled the content of sorting out the documents, and thought of a method that he didn't like.

Because in Chen Zhou's view, all concepts have their own limitations.

Only through the actual proof process, calculation process, and derivation process.

To get real results.

But now, he suddenly wants to try this method.

Whether it works or not...

Anyway, academic research is a process of trial and error.

Chen Zhou picked up the unfinished draft paper in front of him and put it aside.

Then start your own "trial and error" on a new draft paper.

"Try to introduce the concept of abstract K-clusters to simplify some geometric descriptions..."

"Through the introduction of such a concept, the calculation in Shokurov's original proof is simplified..."

But not long after, Chen Zhou crumpled the "trial and error" draft paper in front of him into a ball.

This research method was abandoned by Chen Zhou.

There are two reasons.

One is that Chen Zhou did not see more effective research progress in this method.

The second is that Chen Zhou still feels that this research method is not very reliable.

"Sure enough, this method is not suitable for me..."

Shaking his head slightly, Chen Zhou took back the unfinished draft paper.

Chen Zhou didn't mean that there was anything wrong with such a proof process.

But he just wasn't used to it and didn't like it.

Therefore, from the very beginning, Chen Zhou has been known to the world for his extremely rigorous calculation process.

This method of simplifying calculations does not fit his style very well.

Moreover, Chen Zhou, who is accustomed to using calculations to ensure the correctness of the entire research process, cannot obtain effective feedback through such research methods.

After returning to the research method he was familiar with, Chen Zhou stopped being such a fool.

Everyone's research method is different.

But only the one that suits you and can give full play to your strengths is the best.

You can absorb the strengths of others and turn them into your own use.

However, one should not completely abandon oneself and become someone else.

As time passed, the draft paper in front of Chen Zhou gradually increased.

It's just that there are more scratch paper itself.

Chen Zhou's research on the second problem of the minimal model program has not yet achieved a substantial breakthrough.

Raising his hand, looking at the time, Chen Zhou said helplessly, "Forget it, let's put it down for a while, and watch it tomorrow..."

Just at this moment, a gust of wind blew into the room and scattered the draft paper on the desk.

Chen Zhou hastily went to close the window.

At this time, the sky outside the window had already darkened.

The winter in Yanjing is quite cold.

It was also at noon when Chen Zhou saw that the weather was good, so he opened the window to prepare for ventilation.

As a result, he plunged into the minimal model program and forgot the time and closed the windows.

Reaching out to close the window and draw the curtains, Chen Zhou began to tidy up the draft paper that was blown by the wind.

These draft papers are not just gathered together.

Chen Zhou had to put them away one by one according to the original order.

Although Chen Zhou felt quite annoyed by this, he had no other way.

Who made him love to use A4 draft paper for research?
Instead of doing paperless research on a computer.

Suddenly, Chen Zhou, who was packing up the draft paper, froze in place.

His eyes were fixed on a piece of draft paper he had just picked up.

The content on this draft paper is not the result of "starting from scratch" this afternoon.

It is the content of the literature sorted out at the beginning of the retreat, when the research on the second issue of the minimal model program was carried out.

At this time, Chen Zhou kept thinking about the contents of the miniature model program in his mind.

The content on this draft paper is also intertwined with the content of the minimal model program in his mind.

"I understand……"

At this moment, the originally unclear direction in Chen Zhou's mind became clear.

The original train of thought is also clear at this moment!

He knows the second problem of the minimal model program, how to solve it!
Ignoring the other draft papers still scattered on the ground, Chen Zhou reached out and pulled out the chair, and sat down directly.

Pen cap, unscrew.

New draft paper, lay it on.

The solution to the second problem of the minimal model program begins here!
The passage of time, at this moment, can no longer disturb Chen Zhou's mood.

In his eyes, there are only mathematical symbols that are constantly being written.

In his mind, there is only the clear proof process.

Step by step derivation.

Step by step in depth.

Finally, time stopped at this moment.

The pen also stopped at this moment.

A satisfied smile appeared on Chen Zhou's tired face.

He said softly: "This gust of wind is really timely..."

　Thanks to book friend Yan Hongxue for the 100 starting coins!
　　
　
(End of this chapter)