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

Because this is the content of basic mathematics.

It is about solving 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 often changes.

But if there is a matrix a, the direction of this vector v remains unchanged after linear transformation, just stretching or compressing a certain multiple.

That is, av=λv.

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

The traditional solution here starts by calculating the feature polynomial, then solving the eigenvalue, then solving the homogeneous linear equation system, and finally obtaining the eigenvector.

That's right, this part of the content is just ordinary in the eyes of mathematicians, basic mathematical solution formulas.

However, Chen Zhou found out when calculating the probability of neutrino oscillation.

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

And aren't the three flavors of neutrinos, namely electrons, muons and tauons, equivalent to the transformation between three vectors in space?

Therefore, when studying the topics related to neutrino oscillation, Chen Zhouyi accidentally discovered that there is a more common law between the eigenvector and the eigenvalue.

So, a new and wonderful solution came to Chen Zhou's mind.

"If you know the eigenvalue, you only need to list a simple equation, and the eigenvector can be solved..."

Thinking of this, Chen Zhou kept writing on the draft paper, and began to describe the new formula in his mind.

Chen Zhou has always been a habitual research method for converting physical problems into mathematical problems.

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

Although there is still a lot of distance from solving the problem of neutrino oscillation.

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

"If you create a sub-matrix by deleting the rows and columns of the original matrix..."

"The sub-matrix and the eigenvalues ​​of the original matrix can be combined together to calculate the eigenvectors of the original matrix..."

"You can also get ∣^uαi∣2=(λi-ξα)(λi-xα)/(λi-λj)(λi-λk)..."

Chen Zhou slowly stopped writing and looked at the contents on the draft paper.

He has already obtained the new formula, and there is only a proof process.

The proof process...

Chen Zhou took out a new piece of draft paper again and held the pen in his hand tightly.

The proof begins.

"First define a as an Hermit matrix of nxn, which has the eigenvalue λi(a) and the normal eigenvector vi..."

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

"By deleting jth rows and jth columns, we can obtain the sub-matrix mj of a, with a size of (n-1)×(n-1), and its eigenvalue is λk(mj)....”

"Then, by proof, you can get a Cauchy-Binite formula..."

"Lemma 1 and Lemma 2 can prove..."

“… Through the definition of conjugation, the diagonal element on the left side of Formula 7 determines the submatrix of λi(a)in-a…”

"… Therefore, when applying Lemma 2, the inevitable conclusion is that if an element in the eigenvector disappears, vi,j=0, then the eigenvector equation of matrix a will be transformed into an eigenvector equation of its sub-matrix mj

.”

Chen Zhou's ideas are very clear, and the entire proof process is also very smooth.

Without any obstacles, this new formula was proved.

"It's interesting. No one has noticed this for so long?"

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

If you really want to say it, this new formula is not complicated.

Chen Zhou can also give at least five methods for proofing the new formula.

But why hasn't anyone discovered such a new formula and proof process that is not complicated for so long?

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

This shows that it must be him!

Without him, who knows how long it will take for this formula to remain silent before it can meet the world?

This is not Chen Zhou’s narcissism, but the value of this new formula is indeed quite great.

It has very realistic significance for mathematics, physics, and engineering.

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

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

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

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

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

Chen Zhou had no intention, and immediately sorted out the relevant content of this new formula and published it on the journal.

He just thought that this thing was quite easy to use.

At least, it saves him a lot of trouble in calculating the probability of neutrino oscillation.

If you want to organize it into a paper submission, no matter how you have to wait until he solves the problem of neutrino oscillation.

Chen Zhou satisfactorily packed up this new formula of "studying" and its proof process and put it aside.

Then, I raised my hand and looked at my watch. It was almost noon.

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

Since the time point that proves the new formula is so accurate, there is no need to force the time to delay.

In the afternoon, it is the time for the very small model program.

What is the rotation of physics and mathematics?

As for the time to study and prove the new formula, is it mathematics or physics?

Chen Zhou felt that it should be attributed to physics.

After all, the most direct and effective function of the discovery of the new formula is the study of topics related to neutrino oscillation.

You should know that the calculation problem of neutrino oscillation probability is a core issue in the topics related to neutrino oscillation.

So the time to study new formulas and prove new formulas cannot be counted on the subject of physics?

Chen Zhou, who was sitting at the desk again, found a few pieces from another pile of draft papers and looked at them carefully.

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

This is just the "research manuscript" he completed after he went into seclusion.

He placed the piles of draft papers under his desk.

Otherwise, the desk would have been full.

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

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

The second problem of the Minimal Model Program is not as easy to solve as he expected.

The inspiration brought by Xu Chenyang and the idea that he thought was stable also seemed to have entered a new fork.

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

"The uniqueness of the extremely small model needs to be guaranteed, 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.

Chen Zhou was completely different from him who was full of energy in the morning.

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

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

Suddenly, Chen Zhou reached out and took out a stack of new a4 draft paper.

Unscrew the pen cap and start burying your head in the draft paper.

He intends to re-examine the entire minimalist model program in a new way.

Since you don’t know where the direction is, then go again!
To be continued...