"So what's the problem?"

Fang Chao also expressed his other doubts in the form of scratch paper and dictation.

……

……

"Chao'er, in fact, you don't need these steps at all, from here to here......"

Shen Lang pointed to a few of the steps and said, "These places can be calculated by using the second-order operation method of constant algebra normally, and you can directly skip the seven or eight steps, and you will find that the above derivation is the least squares OLS, and many of the excellent properties of the least squares method can be derived using idempotent matrices, especially the small sample properties, which are basically inseparable from idempotent matrices, such as the simplest, the Pythagorean theorem......"

"If we extend the concept of orthogonal projection to probabilistic spaces, it is the concept of conditional expectation. Any iterative expectation formula or the like can be compared with this orthogonal projection. ”

Shen Lang said as he quickly wrote some equations with a pen.

Fang Chao took a look and saw it at a glance.

It turned out to be this Yazi!

I'm so stupid!

Fang Chao was so annoyed, he was still the first in the class, but he couldn't even understand such a thing at the first time.

It was obviously a very simple thing, but I actually fell into a dead end, and Senior Brother Shen Lang's concise words directly made me pause.

I'm still stupid compared to him.

In mathematics, I am still just a child, even if I won an IMO event with a personal perfect score championship, but compared to Senior Brother Shen Lang, the gap is still too big, maybe Senior Brother Shen Lang did not get a full score back then, it should be that the exam questions are too difficult.

Also, the year I took the exam, I felt quite simple, only one or two stuck me a little bit, but didn't I still hand in the paper early in the limited time?

Besides, in my class, there were a total of four people who got full scores, if it wasn't difficult, how could there be four people who got full marks together?

If there are four people who can get a perfect score, it means that the difficulty is not too great, otherwise, there should not be a perfect score player......

Senior Brother Shen Lang's session, it seems that there is only one perfect score player.

That's right, it must be like this, Senior Brother Shen Lang's examiner who made the question that year 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 by Shen Lang, was hungry and thirsty, and discussed and inquired again.

"If the vector Xt represents the state probability distribution of the t period, according to the Markov hypothesis, the state distribution Xt+1 of the next period is only related to the previous period, which is related to Xt-1 and Xt-2...... It doesn't matter, then you can write the state distribution of the next period as Xt+1=TXt (not txt!! ）。 ”

"where T is the Markov matrix, i.e., the element (i,j) is the probability from state i to state j, and each row adds up to 1."

Like what:

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 steady state? In what way does it manifest itself? Is it a 2D or 3D plane? ”

Shen Langdao, "Using the Morkov chain, then the eigenvalue decomposition of T is a stationary distribution for the eigenvector with an eigenvalue of 1. ”

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

It's like factoring, simplifying a complex formula, but this factoring depends on how you break it down and where you start......

A ternary quadratic equation that you can decompose into binary quadratic ...... Multiple systems of equations are broken down to simplify the problem.

Sometimes tedious steps are made simpler.

The same thing.

Shen Lang just made a point, but did not specifically say what should be done, because the question type of each question will not be the same, it depends on your personal comprehension, and even what kind of opinion you have on different question types.

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

Shen Lang stopped talking, and Fang Chao had no problem.

He is now digesting a series of words that Shen Lang said just now, and even involves the topic that Shen Lang and Professor Lin are jointly studying - the second-order operation method of permanent algebra.

Some places are easy to understand, but some places are really complicated, and with Fang Chao's talent in mathematics, it still takes time to digest, so you can imagine how huge the workload is if this kind of topic wants to be studied thoroughly.

Otherwise, it wouldn't have been Shen Lang and Professor Lin for so long, and it was only the initial stage.

But the academic problems themselves, especially in mathematics, are never solved overnight, and they all require a lot of arithmetic and countless verifications.

Inferences, conjectures, hypotheses, verifications...... Theorem.

There is not a single conjecture that can be turned into a theorem by a single calculation.

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

For example, the Riemann conjecture, even if most mathematicians clearly know that the so-called Riemann conjecture is actually the Riemann theorem, but so what? Have you verified it? After the number of billions of digits, is there a negated prime? Once there is one, then the Riemann conjecture is self-defeating, and it can no longer be called a conjecture or even a theorem.

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

Mathematics is a step-by-step process, and Fang Chao is working hard in this direction.

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

……

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

But with her identity, she was embarrassed to inquire about Fang Chao's news and asked him why he didn't come to the playground to exercise in the past few days......

Because once you ask, it will make outsiders think that they care about Fang Chao and have a boyfriend and girlfriend relationship with him.

They are not, at most, they have some good feelings for each other, but when it comes to men and women...... How shy, no one has been chased yet, how can 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 busy with lately? I can't see you on the playground, and if you don't show up, I won't count the meal I owe you. ”

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