hahhaah 29:53 "i think of matrices as people at this point". As we approach the end of the course, i just want to thank you AGAIN, amongst the plethora of other appreciations. This have been a remarkable journey, I dont think any other lecturer in the entire world would have made this as enjoyable as you have Mr Strang. Case-in-point: the comment at this time stamp just adds that additional layer of novelty and enjoyment that makes the whole experience just remarkable.
I enjoyed this lecture on Similar Matrices and Jordan Form as part of linear algebra. Once again DR. Strang showed the application of both topics with examples.
Outstanding Gill! I studied LA 40 years ago, but it was a mere 2 dimensional projection of the many dimensions you present. I bought your book and donated all my other LA texts. You're an excellent instructor.
I LOVE GILBERT STRANG SIR. I am in high school and love his lectures. All this is taught in a boring way in our class...but STRNG SIR maks this topic epic. Now I love linear algebra!! thanks a lot MIT for helping millions like me
Pure gold. Amazing to hear that emphasis in LinAlg has been shifting until so recently (Jordan out of fashion, SVD to the forefront). Because of computational characteristics?
'who wouldn't ?' Those who actually want to learn something about Jordan Form would set your time machine to T-20 [years]. At the very least, the title of the lecture is misleading.
At around 8:57, professor says that only zero vector leads to zero in the inequality, which is wrong. Because as long as x is in the nullspace of A, the equal sign will be reached in the inequality
So how many families are there with more than just 2 repeated roots? The example of 4 repeated roots showed 2 different Jordan decompositions, one with a size 3 and size 1 jordan block, and then another with two size 2 jordan blocks. They are not similar. What's the partition law for the number of families of similar matrices with d repeated roots? Is there a connection with group theory? How about multiple groups of repeated roots? for 2x2 matrices, there's 2 cases: unique and single family of similar matrices, or single repeated eigenvalue and 2 families, the scaled identity, and the remaining family similar to the jordan form. How many families for 3x3, 4x4, etc matrices? curious...
Why is that a pos def matrix never has an "unsuitably small" value in a pivot? I get that the pivots will never be 0's since it is a pos def. But how do we know about the unsuitably small part of that statement?
@@mitocw Thank you very much for going through the trouble to fix the audio channels and reupload, it's nice that these videos still get love from MIT after all these years, because us students definitely need them!
10:30 shouldn't the rank of A^TA be m, so that the it's nullspace is only the nullvector? If A∈M(m x n, R) so A^TA∈M(m x m, R), right?. Hence the rank should be m. Can someone confirm this to me?
I won't blame my professor, he had to teach the entire course from his home during lockdown, but this is an entirely different (and clearer) approach to the subject
Audio channels fixed!
thanks you
@@sanketneema286 yup
I love MIT man, this university and people here are so phenomenal
hahhaah 29:53 "i think of matrices as people at this point". As we approach the end of the course, i just want to thank you AGAIN, amongst the plethora of other appreciations. This have been a remarkable journey, I dont think any other lecturer in the entire world would have made this as enjoyable as you have Mr Strang. Case-in-point: the comment at this time stamp just adds that additional layer of novelty and enjoyment that makes the whole experience just remarkable.
45:28 "I'm very positive about positive definite matrices." This is epic.
12:11 similar matrices
31:10 Jordan Form
Thank you!
So excited for SVD coming up! Been following the course just for SVD and it going to be the next one!😄
I enjoyed this lecture on Similar Matrices and Jordan Form as part of linear algebra. Once again DR. Strang showed the application of both topics with examples.
The way Mr Strang asks Why? Each Time a new case comes up just wins my heart with his innocence and curiosity .
"I think of these matrices as people". thank you so much professor to making me feel the same.
you made me love linear algebra
Does this like was from Gilbert Strang??❤️❤️❤️❤️
@@ashwinjain6787 yes
@@aashnajain6519 this like was really from Gilbert Strang sir???
@@ashwinjain6787 i think, from the one who is managing MIT TH-cam channel :D
@@aashnajain6519 Are you a student ?? I feel yes because why would be a person will see such a great lecture!!!
Outstanding Gill! I studied LA 40 years ago, but it was a mere 2 dimensional projection of the many dimensions you present. I bought your book and donated all my other LA texts. You're an excellent instructor.
Lecturing capability aside, the thing that amazes me most about this man is his entrancing hand-writing! They just don't make em like they used to!
"You can come even after monday", man he is just on a another level.
I LOVE GILBERT STRANG SIR. I am in high school and love his lectures. All this is taught in a boring way in our class...but STRNG SIR maks this topic epic. Now I love linear algebra!! thanks a lot MIT for helping millions like me
nigga, linear algebra and high school?
@@chiragraju821 vectors determinants etc. We do have
aditya 17 #doubt
@@Brien831 not surprising. Used to be A level FP3 edexcel or core for IB further math
Calculus BC ain't really much at all lmao
@@chiragraju821 hello
Pure gold. Amazing to hear that emphasis in LinAlg has been shifting until so recently (Jordan out of fashion, SVD to the forefront). Because of computational characteristics?
Now I regret not watching all of his videos although I knew they were available and great videos!
I've always heard "Jordan" as kind of shoes but after this Wonderful Lecture I can see sth !! THANKS PROF. STRANG
"Please come on Monday" : Jeez if I could time travel, I'd get there somehow. who wouldn't ?
'who wouldn't ?' Those who actually want to learn something about Jordan Form would set your time machine to T-20 [years].
At the very least, the title of the lecture is misleading.
Well you can sort of, by watching the lecture 29 :-)
37:09 "If you want nightmares, think about matrices like these!" - Prof. Strang😆
minute 19:00 was very funny! such a sweet teacher, I wish I had a teacher like that! The best Linear Algebra Course in the history of men!
At around 8:57, professor says that only zero vector leads to zero in the inequality, which is wrong. Because as long as x is in the nullspace of A, the equal sign will be reached in the inequality
the thing about one family hit me hard
An absolute legend. Thank you so much for such great lectures.
The video was awesome. Now it is perfect.
(Now my left ear can be as intelligent as my right ear.)
12:11 for similar matrices
Jordan Form in 31:10
So how many families are there with more than just 2 repeated roots? The example of 4 repeated roots showed 2 different Jordan decompositions, one with a size 3 and size 1 jordan block, and then another with two size 2 jordan blocks. They are not similar. What's the partition law for the number of families of similar matrices with d repeated roots? Is there a connection with group theory? How about multiple groups of repeated roots? for 2x2 matrices, there's 2 cases: unique and single family of similar matrices, or single repeated eigenvalue and 2 families, the scaled identity, and the remaining family similar to the jordan form. How many families for 3x3, 4x4, etc matrices? curious...
Many thanks!
Best teacher
helped so much thanks!!
ayyeeee! I got this one!
I enjoyed this
Legend
Took me some time to realize he was talking about the American version of 'football'.
Is he American?
Why is that a pos def matrix never has an "unsuitably small" value in a pivot? I get that the pivots will never be 0's since it is a pos def. But how do we know about the unsuitably small part of that statement?
The statement about my questions is at 10:38
great video.
Not as many comments. Did we lose some ppl somewhere???
The video was re-uploaded recently to fix an audio channel problem.
@@mitocw Thank you very much for going through the trouble to fix the audio channels and reupload, it's nice that these videos still get love from MIT after all these years, because us students definitely need them!
Looks like I were at MIT.
40:36 why second matrix is not similar to the first? Is there a simple way to show that it does not exist such M, that M^-1 A M = B?
It's not obvious. He's using the theorem that they can only be similar if they have the same Jordan form.
Thanks!
10:30 shouldn't the rank of A^TA be m, so that the it's nullspace is only the nullvector? If A∈M(m x n, R) so A^TA∈M(m x m, R), right?. Hence the rank should be m. Can someone confirm this to me?
ok nvm. it's gonna be a n x n matrix
Bruh our university has his book as a recommendation lol
We use his book
36:02
29:53 :')
If this is linear algebra. I don't know what rubbish they are teaching in schools and colleges.
I won't blame my professor, he had to teach the entire course from his home during lockdown, but this is an entirely different (and clearer) approach to the subject