Inner & outer products | Lecture 5 | Matrix Algebra for Engineers
Definition of an inner and outer product of two column vectors.
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Lecture notes at www.math.ust.hk/~machas/matrix...
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Пікірлер: 132
Find other Matrix Algebra videos in my playlist kzread.info/head/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx
@stearin1978
2 жыл бұрын
It would be nice to write here Inertia tensor in the form Sum (x^Tx) I - xx^T. Both 2 products in one basic physical entity. Nice video anyway.
thanks sir I am from India i need to know about inner and outer multiplication during programming you helped me very well once again thank you sir
man this is quality teaching here. you my friend can call you a teacher unlike a lot of other "teachers"
So helpful. Thank you for making such high quality lectures available to everyone. Much appreciated.
This clears a lot of my doubts as I am learning SVM kernels. Thanks Jeff!!
High quality lectures that are short, easy to understand, and can be applied to many situations. Thank you very much.
Dont think there is a better teacher than this, thank you.
Good stuff and love the format! Thank You!
You are a great teacher. Totally textbook.
Clear, short and to the point. Thanks.
In this short video, very clear and helpful. Thanks a lot.
I like your way of presentation. It's as if you are enlightening as from abyss.
Your explanation was awesome Sir!....
Thanks....very much i have understood the concept and your video is far much clear....if possible i would like to see your videos on solving problems in linear algebra and analytical geometry if you do present thanks
Thanks for clear informative video. Helped a lot
Great video. Thank you
Your coursera course was fantastic. Thank you!
@nature_through_my_lens
2 ай бұрын
Which one?
Thanks professor- great explanation.
Very Beautifully Explained.
Thanks Jeff, you're amazing!!
You saved me. Thanks for the to the point video.
really helpful! respected prof.
Thank you for this material, I am currently learning Matrix Factorization algo, its hard to understand it but it turn out Im just missing this fundamental concept about outer product.
Thanks Jeffrey I really appreicate this series. I am taking graduate level Machine Learning class and have never taken linear algebra before. I know, stupid. I tired watching 3blue1brown's series which is a short 17 lectures series that is great was very interesting but not perfect for my needs. Than I tried watching the 144 video khan series on linear algebra. I got to video 32 lol. good, but once again not perfect for my needs. Thank god I found you! Perfect for what I need right now. Thanks so much I was feeling pretty helpless until I ran into this.
@tdpro3607
2 жыл бұрын
3b1b only focus on the irl uses and visualisation, as he states that there are already many resources out there that teach you how to compute things
@Leila0S
2 жыл бұрын
I'm now in your same situation and did your same steps and thankfully I found this playlist and another channel's linear algebra playlist very satisfactory.
Chasnov is a really cool title for a maths teacher.
This is such a great video thank you.
Thanks to the transpose operator, without qualifying further, a 'vector in R^n' is a column vector or nx1 matrix, and a 'row vector in R^n' or 1xn matrix would just be the transpose of the nx1 column vector.
It's so clear, thank you so much!
You’re great. Thank you!
Thanks Jeffrey!
Thank you so much
U just wrapped it up, thanks alot
I bought your “ Matrix Algebra for engineers” on coursera and I found it so helpful!! Thank you so much! Can you do more intermediate/advanced matrix algebra courses?
@ProfJeffreyChasnov
5 жыл бұрын
Thanks! I am working on a vector calculus course now. Maybe you can find other more advanced linear algebra courses on Coursera or EdX? Or on MIT open courseware?
@JulieIsMe824
5 жыл бұрын
Jeffrey Chasnov Haha...I’m so excited you replied!!! Thank you so much for the advice!
@abhisheksahu616
5 жыл бұрын
Thanks, am going to check this one now.
@subhashbhambhu8792
4 жыл бұрын
Hii
Thank you very much this is very insightful and useful, are you by chance going to do algorithms?
Thanks a lot
Thanks🙏
Thank you so much.
Well explained, thanks!
Good work.
thank you for that wonderful explanation..:D
Thanks
Thank you so much, good man
Awesome video
thanks!
Great!!
Thank-you
thanks
Thanks professor
thank you so much
Thanks!!
Thanks well method
It would definitely make sense to add the norm of the inner product = ||u|| ||v|| cos(alpha), where alpha is the angle between two vectors - a simple and clear geometric interpretation.
@ProfJeffreyChasnov
4 жыл бұрын
This comes early in my vector calculus class.
really helpful
very helpful!
How do you film these videos? I assume you're not actually writing backwards. Are you filming yourself from both the back and front and then overlaying the individual videos?
@ProfJeffreyChasnov
5 жыл бұрын
Video is shot through the glass, and the software mirror reverses the writing.
@ccuuttww
5 жыл бұрын
I would say this is linear transformation in linear algebra --- The reflection are u using left hand for writing?
@magmasceptre
5 жыл бұрын
I think he just puts the camera on the other side of the glass pane and he would write on the other side. After which the video will be flipped left to right.
@Vicky-pb5hg
5 жыл бұрын
You may wish to read about "Lightboard", invented by Prof. Michael Peshkin of Northwestern University.
@MONKEYDUDE2701
4 жыл бұрын
bruh he just mirrors the whole Video bro.
super helpful
Subscribed!
jeff bezos is that you?
@zurzakne-etra7069
3 жыл бұрын
jeff bezoz (mr union buster) could never
@BrickBreaker21
3 ай бұрын
Jeff Bezos is Walmart Jeff Chaznov
Did you really learn how to mirror your writing? Excellent video, thank you!
@ProfJeffreyChasnov
Жыл бұрын
kzread.info/dash/bejne/iXaTpcOkoajSgZM.html
Muito bom 👏👏👏
thx
I love how he just walks away at the end casually
Thank you, Jeffrey! Could you please tell us how the outer product can be helpful in ML or, at least, indicate the video where you tackle this subject?
what is the system that you use here to explain the courses
Excellent teaching! 😂
what if the transpose of V has multiple rows? How do we compute the outer product?
Besttt
what are the original and strong definition of inner product . can u guide me about this topic. sir,
Hello from Uzbekistan
I'm trying to find the meaning to the outer product, the calculation is trivial but you tease that the matrix has low dimensionality. This is what i need to know but I can go through an entire engineering course just to know this one thing when I'm not an engineer... Anyway, was an excellent lesson, thank you.
what is said in hours is said in 9 minutes! thanks
more topics?
Jeffery can we apply these rules to square matrices for example? Peter
@ProfJeffreyChasnov
3 жыл бұрын
This video is about column and row vectors.
33 slides or 1 screen this is lit
cf. outer product vs. tensor product?
That's fine for row and column vectors, but what would be the outer product of two 2X2 matrices?
@ProfJeffreyChasnov
4 жыл бұрын
It's only defined for vectors.
@MrSidTaylor
4 жыл бұрын
@@ProfJeffreyChasnov Would that be the tensor product?
@ProfJeffreyChasnov
4 жыл бұрын
@@MrSidTaylor Yes
he writes backwards so well lol
what is that dot product tho?
How can he write it like this
did he actually have a glass in front?
Oh he is actually writing it all in mirror :)
@bastienp7334
Жыл бұрын
oooh no i guess the video is mirrored 🤯 if i were to do that i would actually write in mirror because it's more fun hehe
@ProfJeffreyChasnov
Жыл бұрын
@@bastienp7334 kzread.info/dash/bejne/iXaTpcOkoajSgZM.html
@bastienp7334
Жыл бұрын
@@ProfJeffreyChasnov Hahaha thanks
Mmmm😊
Hope, am not the only person to suddenly see Jeff Bezos, and then realised.. Good teaching
One Pen Man
GG
why uTv becomes a 3,1 and uvT becomes a 3,3,...??
@RealLifeKyurem
4 жыл бұрын
Nat Serrano vector and matrix multiplication are not commutative. u·v produces a scalar, because u^T is a 3×1 matrix, while v is a 1×3 matrix. (3×1)(1×3) = 1×1. So no, u·v doesn’t produce a 3×1 matrix. u×v produces a matrix, because u is a 1×3 matrix, while v^T is a 3×1 matrix. (1×3)(3×1) = 3×3.
0 intuition, just formulas yet useful
Are you left-handed or right-handed ?
@ProfJeffreyChasnov
5 жыл бұрын
right
@OprichnikStyle
4 жыл бұрын
too good to be true
@-long-
4 жыл бұрын
check this kzread.info/dash/bejne/qXeD19dpXdKbiaw.html
Did anyone else mishear u2 as KZread 😂😂
how this guy writes that way ????!!!!
wow, Jeff Bezos teaching math
Am I the only one who thinks he that he sounds like Yondu
how tf is this man writing this? he can write backwards??
thank you jeff bezos
@blueice1364
4 жыл бұрын
I think all the white bald guys are named the same...
thanks