Become a master from now on

Chapter 245 Communication (seeking subscription monthly pass!)
"So what's the problem?"

Fang Chao also expressed his other doubts in the form of draft paper plus dictation.

……

……

"Chao'er, actually you don't need these steps at all. From here to here..."

Shen Lang pointed to some of the steps and said, "These places can be calculated by normal algebraic second-order operations, and seven or eight steps can be skipped directly, and you will find that, The above derivation is the least square method OLS. Many excellent properties of the least square method can be derived using idempotent matrices, especially the small sample properties, basically inseparable from idempotent matrices, such as the simplest, Pythagoras Stein theorem..."

"If the concept of orthogonal projection is extended to probability space, it is the concept of conditional expectation. Any iterative expectation formula can be compared with this orthogonal projection."

As Shen Lang spoke, he quickly wrote some equations with a pen.

Fang Chao saw it clearly at a glance.

It turned out to be this Yazi!
I am so stupid!

Fang Chao was very upset. Fortunately, he was still No. 1 in the class, but he couldn't even understand such a thing immediately.

It was a very simple thing, but I actually fell into a dead end, and the concise words of senior brother Shen Lang directly made me suddenly enlightened.

Compared to him, I'm still too stupid.

In terms of mathematics, I am still just a child. Even if I have won a personal full-score champion in an IMO event, the gap is still too big compared to Senior Brother Shen Lang. Maybe Senior Brother Shen Lang did not get a full score back then. The result, it should be that the exam questions of that year were too difficult.

That's right, I felt that the exam was quite easy, only one or two questions stuck me a little bit, but didn't I still hand in the papers early within the limited time?
Besides, in my class, a total of four people got full marks. If it was not difficult, how could it be possible for four people to get full marks together?
There are four people who can get full marks, which means that the difficulty is not too high, otherwise, there shouldn't be a player with full marks...

In Senior Brother Shen Lang's class, there seemed to be only one player with a perfect score.

That's right, it must be like this. The examiner who made the test for Senior Brother Shen Lang was a pervert. Otherwise, with Senior Brother Shen Lang's level, it should be very easy to get a full score.

So Fang Chao, who was satisfied with Shen Lang's side, was eager to discuss and ask again.

"If the vector Xt represents the state probability distribution of period t, according to the Markov assumption, the state distribution Xt+1 of the next period is only related to the previous period, and has nothing to do with Xt-1, Xt-2... , then the state distribution of the next period can be written as Xt+1=TXt (not txt!!!).”

"Where T is a Markov matrix, that is, the (i, j)th element is the probability from state i to state j, and the sum of each row is equal to 1."

such as:

T=[0.8 0.1 0.1]
T=[0.2 0.6 0.2]
T=[0.1 0.1 0.8]
"When t tends to infinity, what is the stable state? How does it appear? In two-dimensional or three-dimensional surface?"

Shen Langdao, "Using the Morkov chain, then decompose T into eigenvalues, and the eigenvector with an eigenvalue of 1 is a stationary distribution."

When Fang Chao heard this, he realized it in an instant.

This is just like factoring, simplifying a complex formula, but this factoring depends on how you decompose it and where to start...

For ternary quadratic equations, you can decompose it into binary quadratics... Multiple equations are decomposed to simplify the problem.

Sometimes tedious steps are for simplicity.

The same is true.

Shen Lang just made a point, but did not say how to do it specifically, because the question types of each question are different, it depends on your personal comprehension, and even what kind of views you have on different question types .

But these are not problems in Shen Lang's view, as long as Fang Chao tells the general idea, with Fang Chao's talent, it is too easy to turn these things into his own.

Shen Lang stopped talking, Fang Chao had no problem.

He is now digesting the series of words that Shen Lang said just now, and it even involves the subject that Shen Lang and Professor Lin have studied together - the second-order calculation method of constant algebra.

Some places are easy to understand, but some places are indeed complicated. Considering Fang Chao's talent in mathematics, it still takes time to digest it. One can imagine how much work is required to thoroughly study this kind of subject. huge.

Otherwise, Shen Lang and Professor Lin would not have spent such a long time and it was only the initial stage.

But the academic problem itself is like this, especially in mathematics, which has never been solved overnight. It requires a lot of arithmetic and countless verifications.

Inferences, conjectures, assumptions, verifications...theorems.

No conjecture can be turned into a theorem with just one calculation.

Behind every theorem are hundreds, thousands of formulas, which are then turned into an equation to complete a theorem.

For example, Riemann's conjecture, even if most mathematicians know that the so-called Riemann's conjecture is actually Riemann's theorem, but so what?Have you verified it?Is there a negated prime number after the billionth digit of the number?Once there is one, then the Riemann conjecture will be self-defeating, and it can no longer be called a conjecture or even a theorem.

But so far, after so many years, countless mathematicians have been trapped on this conjecture, and have not yet come up with an answer.

Mathematics is a gradual process, and Fang Chao is working hard in this direction.

Shen Lang got up, made himself a cup of fragrant coffee, and was fascinated by the scenery outside the hotel window for a moment.

……

Zhang Ling hadn't seen Fang Chao on the playground for several days, and was somewhat worried about him for a while.

But with her identity, she was embarrassed to inquire about Fang Chao and ask him why he didn't come to the playground to exercise these days...

Because if you ask, it will make outsiders think that you care about Fang Chao and that you are boyfriend and girlfriend.

They are not, at most, they have a certain affection for each other, but when it comes to men and women...how shy, they have not been chased yet, how could they be together.

So after many ideological struggles, Zhang Ling sent a message to a friend named 'Yi Yang Qianxi'.

"Senior, what have you been up to lately? I can't even see you on the playground. If you don't show up for the meal I owe you, you won't count."

(End of this chapter)