Markov Matrices

MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: ocw.mit.edu/18-06SCF11
Instructor: David Shirokoff
A teaching assistant works through a problem on Markov matrices.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@user-fr1we2xk9u]

Herein we observe an advantage of being left-handed. :)

[@boruiwang1738]

Huge thanks to you!! Very clearly explained at a comfort pace. Its nearly final and my teacher's only covering the theorems and some calculation examples. This mit series really showed me what matrices could achieve and the connection between concepts. (I especially like the fibonacci part and this partical part) Good job!

[@prajyot2021]

Such brief and impeccable lecture
Totally enjoying it

[@nilslorand]

love his enthusiasm :)
Good video

[@surajmirchandani4613]

Best one yet. Really cleared everything up in this chapter.

[@user-jz6ou6ce1z]

So interesting lecture and problem on Markov matrix!

[@benbug11]

Very well explained, thank you

[@ankanghosal]

Very helpful video. Thanks mit

[@Maunil2k]

Very well explained !!

[@Amit.58]

Wow quite amazing problem❤❤❤

[@AnupKumar-wk8ed]

Very good video and very clearly explained.

[@abhilast6629]

Hey Indian bro do you love mathematics?

[@AnupKumar-wk8ed]

@@abhilast6629 Sure I do.

[@stephenclark9917]

The Markov matrix A is a transpose of what is usually presented.

[@fedepan947]

Thank you! Good explanation.
But I think it is not necessary to calculate the decomposition A = UDU-1.
We know that the probability after k steps is Pk = c(λ1)(^k)x1 + d(λ2)(^k)x2 where x1 and x2 are the eigenvectors and λ1, λ2 the eigenvalues, with P0 we can calculate the coefficients c and d for k=0. After 100 steps the probability is Pk for k = 100.

[@dexterity3696]

Definitely, maybe he hasn't taken the course by prof. Strang. LOL

[@thedailyepochs338]

lol i was expecting him to that and he never did

[@thedailyepochs338]

@@dexterity3696 he definitely didn't, if he did he would have named the eigenvector S and the diagonal eigenvalue matrix capital Lambda

[@nprithvi24]

I guess the main point of recitation is not just to solve for an answer but make students recall previous methods discussed in the class. For example, calculating the inverse of a matrix part was relatively discussed 3-4 lectures before this one and there's a good chance students might have forgot about it. This tutorial was a good refresher.

[@federizz686]

Love this

[@kostikoistinen2148]

This guy can explain things well. He says, "Welcome back." Now I’m trying to find the first video for which this video is a sequel. Could someone tell me where that first video is?

[@mitocw]

The RUclips playlist for the course: ruclips.net/p/PL221E2BBF13BECF6C. The course materials on MIT OpenCourseWare: ocw.mit.edu/18-06SCF11. Best wishes on your studies!

[@cssaziado]

Thank you, m7

[@peterhind]

So I sort of understand right until the end. With the final probability for n = infinity, being one third, one in two; how does that translate to the answer to the question 'What is the probability it is at A and B after an infinite number of steps'. Is the answer that it's six more times as likely to be at B than A ?

[@Oleg86F]

We start with matrix A and vector p0=(1,0) - meaning 100% probability particle in the point A. After infinite number of steps (which are A^n * p0 we approaching to the vector (1/3, 2/3) which means : particle in point A- 1/3 (~33% probability) particle in point B - 2/3 (~67% probability)

[@peterhind]

@@Oleg86F Thanks, It's making more sense now

[@theodorechan4343]

this was great

[@ricardoV94]

I get different eigenvalues: (1, -0.2)

[@GoatzAreEpic]

ty fam

[@richard_guang]

This guy reminds me of Will from good Will hunting

[@fackarov9412]

cool

[@EmanuelCohen-HenriquezCiniglio]

Goat

[@user-em4vq5cy4x]

gg

[@reginalnzubehimuonaka6659]

For an MIT solution, it lacks some proof. We do not always see, we need a detailed explanation.
But it is fine.