Inner & outer products | Lecture 5 | Matrix Algebra for Engineers

Definition of an inner and outer product of two column vectors.
Join me on Coursera: imp.i384100.net/mathematics-f...
Lecture notes at www.math.ust.hk/~machas/matrix...
Paperback at www.amazon.com/Matrix-Algebra...
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Пікірлер: 132

  • @ProfJeffreyChasnov
    @ProfJeffreyChasnov4 жыл бұрын

    Find other Matrix Algebra videos in my playlist kzread.info/head/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx

  • @stearin1978

    @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.

  • @harsh_rana
    @harsh_rana3 жыл бұрын

    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

  • @MONKEYDUDE2701
    @MONKEYDUDE27014 жыл бұрын

    man this is quality teaching here. you my friend can call you a teacher unlike a lot of other "teachers"

  • @alimurad5312
    @alimurad53123 жыл бұрын

    So helpful. Thank you for making such high quality lectures available to everyone. Much appreciated.

  • @spontaneousbagpacker9447
    @spontaneousbagpacker94474 жыл бұрын

    This clears a lot of my doubts as I am learning SVM kernels. Thanks Jeff!!

  • @theman2449
    @theman2449 Жыл бұрын

    High quality lectures that are short, easy to understand, and can be applied to many situations. Thank you very much.

  • @karam3045
    @karam30453 жыл бұрын

    Dont think there is a better teacher than this, thank you.

  • @rationalistfaith
    @rationalistfaith5 жыл бұрын

    Good stuff and love the format! Thank You!

  • @dagraves
    @dagraves2 жыл бұрын

    You are a great teacher. Totally textbook.

  • @mikejason3822
    @mikejason38223 жыл бұрын

    Clear, short and to the point. Thanks.

  • @LuciaSilva-ek3qr
    @LuciaSilva-ek3qr3 жыл бұрын

    In this short video, very clear and helpful. Thanks a lot.

  • @sajithk9650
    @sajithk96502 жыл бұрын

    I like your way of presentation. It's as if you are enlightening as from abyss.

  • @RestartUPSC2026
    @RestartUPSC20264 жыл бұрын

    Your explanation was awesome Sir!....

  • @kelvinmaina1189
    @kelvinmaina11894 жыл бұрын

    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

  • @chillynights4055
    @chillynights40554 жыл бұрын

    Thanks for clear informative video. Helped a lot

  • @AJ-et3vf
    @AJ-et3vf Жыл бұрын

    Great video. Thank you

  • @kiichitakeuchi
    @kiichitakeuchi4 жыл бұрын

    Your coursera course was fantastic. Thank you!

  • @nature_through_my_lens

    @nature_through_my_lens

    2 ай бұрын

    Which one?

  • @saschaffer
    @saschaffer3 жыл бұрын

    Thanks professor- great explanation.

  • @29ibrahimsayed95
    @29ibrahimsayed952 жыл бұрын

    Very Beautifully Explained.

  • @nikhilaryal
    @nikhilaryal3 жыл бұрын

    Thanks Jeff, you're amazing!!

  • @hitesh_sewani
    @hitesh_sewani Жыл бұрын

    You saved me. Thanks for the to the point video.

  • @allanshu177
    @allanshu1775 жыл бұрын

    really helpful! respected prof.

  • @hafidhrendyanto2690
    @hafidhrendyanto2690 Жыл бұрын

    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.

  • @danielgray8053
    @danielgray80533 жыл бұрын

    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

    @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

    @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.

  • @Heroni66a
    @Heroni66a Жыл бұрын

    Chasnov is a really cool title for a maths teacher.

  • @parsakei9006
    @parsakei90062 жыл бұрын

    This is such a great video thank you.

  • @xoppa09
    @xoppa093 жыл бұрын

    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.

  • @zhuoyuelyu
    @zhuoyuelyu3 жыл бұрын

    It's so clear, thank you so much!

  • @EllisAlcantara
    @EllisAlcantara3 жыл бұрын

    You’re great. Thank you!

  • @alpsahin4340
    @alpsahin43405 жыл бұрын

    Thanks Jeffrey!

  • @shreyaskumarm3534
    @shreyaskumarm35342 жыл бұрын

    Thank you so much

  • @ahmedmuhammed6905
    @ahmedmuhammed69052 жыл бұрын

    U just wrapped it up, thanks alot

  • @JulieIsMe824
    @JulieIsMe8245 жыл бұрын

    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

    @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

    @JulieIsMe824

    5 жыл бұрын

    Jeffrey Chasnov Haha...I’m so excited you replied!!! Thank you so much for the advice!

  • @abhisheksahu616

    @abhisheksahu616

    5 жыл бұрын

    Thanks, am going to check this one now.

  • @subhashbhambhu8792

    @subhashbhambhu8792

    4 жыл бұрын

    Hii

  • @ahmedelmattawaa5029
    @ahmedelmattawaa5029 Жыл бұрын

    Thank you very much this is very insightful and useful, are you by chance going to do algorithms?

  • @bilalabbad7954
    @bilalabbad79542 жыл бұрын

    Thanks a lot

  • @ASHNAY9
    @ASHNAY93 жыл бұрын

    Thanks🙏

  • @blueice1364
    @blueice13644 жыл бұрын

    Thank you so much.

  • @Baron-digit
    @Baron-digit3 жыл бұрын

    Well explained, thanks!

  • @JimmyXC234
    @JimmyXC2342 жыл бұрын

    Good work.

  • @nikhilnarayane680
    @nikhilnarayane6804 жыл бұрын

    thank you for that wonderful explanation..:D

  • @RualddeBruyn
    @RualddeBruyn2 жыл бұрын

    Thanks

  • @kevindave277
    @kevindave277Ай бұрын

    Thank you so much, good man

  • @Rudrazz
    @Rudrazz3 жыл бұрын

    Awesome video

  • @NovaWarrior77
    @NovaWarrior772 жыл бұрын

    thanks!

  • @user-gb6qw4yv7p
    @user-gb6qw4yv7p3 жыл бұрын

    Great!!

  • @ndngdippchn
    @ndngdippchn5 жыл бұрын

    Thank-you

  • @shymaaabdelkhaleq7254
    @shymaaabdelkhaleq72543 жыл бұрын

    thanks

  • @Edioteditor
    @Edioteditor4 жыл бұрын

    Thanks professor

  • @tadeletekeba13
    @tadeletekeba134 жыл бұрын

    thank you so much

  • @abhishek_sengupta
    @abhishek_sengupta3 жыл бұрын

    Thanks!!

  • @user-tr9be1jb7i
    @user-tr9be1jb7i2 жыл бұрын

    Thanks well method

  • @vanilin113
    @vanilin1134 жыл бұрын

    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

    @ProfJeffreyChasnov

    4 жыл бұрын

    This comes early in my vector calculus class.

  • @ashutoshjha225
    @ashutoshjha2253 жыл бұрын

    really helpful

  • @maartjet6906
    @maartjet69062 жыл бұрын

    very helpful!

  • @eric5258
    @eric52585 жыл бұрын

    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

    @ProfJeffreyChasnov

    5 жыл бұрын

    Video is shot through the glass, and the software mirror reverses the writing.

  • @ccuuttww

    @ccuuttww

    5 жыл бұрын

    I would say this is linear transformation in linear algebra --- The reflection are u using left hand for writing?

  • @magmasceptre

    @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

    @Vicky-pb5hg

    5 жыл бұрын

    You may wish to read about "Lightboard", invented by Prof. Michael Peshkin of Northwestern University.

  • @MONKEYDUDE2701

    @MONKEYDUDE2701

    4 жыл бұрын

    bruh he just mirrors the whole Video bro.

  • @pearechen5111
    @pearechen51113 жыл бұрын

    super helpful

  • @mauricioalfaro9406
    @mauricioalfaro94062 жыл бұрын

    Subscribed!

  • @eldraco252
    @eldraco2524 жыл бұрын

    jeff bezos is that you?

  • @zurzakne-etra7069

    @zurzakne-etra7069

    3 жыл бұрын

    jeff bezoz (mr union buster) could never

  • @BrickBreaker21

    @BrickBreaker21

    3 ай бұрын

    Jeff Bezos is Walmart Jeff Chaznov

  • @jamessterling955
    @jamessterling955 Жыл бұрын

    Did you really learn how to mirror your writing? Excellent video, thank you!

  • @ProfJeffreyChasnov

    @ProfJeffreyChasnov

    Жыл бұрын

    kzread.info/dash/bejne/iXaTpcOkoajSgZM.html

  • @princesatartaruga444
    @princesatartaruga4443 жыл бұрын

    Muito bom 👏👏👏

  • @fwsgsdg1977
    @fwsgsdg19773 ай бұрын

    thx

  • @akshaankaware1787
    @akshaankaware17873 жыл бұрын

    I love how he just walks away at the end casually

  • @alexandradobrescu8795
    @alexandradobrescu87953 жыл бұрын

    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?

  • @eylmaz6696
    @eylmaz66964 жыл бұрын

    what is the system that you use here to explain the courses

  • @curtpiazza1688
    @curtpiazza16883 ай бұрын

    Excellent teaching! 😂

  • @xCarbon02
    @xCarbon023 жыл бұрын

    what if the transpose of V has multiple rows? How do we compute the outer product?

  • @anshukalshyan5967
    @anshukalshyan5967 Жыл бұрын

    Besttt

  • @ALIRAZA-zv5mn
    @ALIRAZA-zv5mn2 жыл бұрын

    what are the original and strong definition of inner product . can u guide me about this topic. sir,

  • @abboszaitov2093
    @abboszaitov20933 жыл бұрын

    Hello from Uzbekistan

  • @davidmurphy563
    @davidmurphy5632 жыл бұрын

    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.

  • @magdynasr6639
    @magdynasr66393 жыл бұрын

    what is said in hours is said in 9 minutes! thanks

  • @ccuuttww
    @ccuuttww5 жыл бұрын

    more topics?

  • @petelok9969
    @petelok99693 жыл бұрын

    Jeffery can we apply these rules to square matrices for example? Peter

  • @ProfJeffreyChasnov

    @ProfJeffreyChasnov

    3 жыл бұрын

    This video is about column and row vectors.

  • @JVenom_
    @JVenom_ Жыл бұрын

    33 slides or 1 screen this is lit

  • @ytpah9823
    @ytpah98233 жыл бұрын

    cf. outer product vs. tensor product?

  • @MrSidTaylor
    @MrSidTaylor4 жыл бұрын

    That's fine for row and column vectors, but what would be the outer product of two 2X2 matrices?

  • @ProfJeffreyChasnov

    @ProfJeffreyChasnov

    4 жыл бұрын

    It's only defined for vectors.

  • @MrSidTaylor

    @MrSidTaylor

    4 жыл бұрын

    @@ProfJeffreyChasnov Would that be the tensor product?

  • @ProfJeffreyChasnov

    @ProfJeffreyChasnov

    4 жыл бұрын

    @@MrSidTaylor Yes

  • @austinosogwin4121
    @austinosogwin41213 жыл бұрын

    he writes backwards so well lol

  • @stefanosmitsios7694
    @stefanosmitsios76942 жыл бұрын

    what is that dot product tho?

  • @-error-404
    @-error-4049 ай бұрын

    How can he write it like this

  • @matgg8207
    @matgg82072 жыл бұрын

    did he actually have a glass in front?

  • @bastienp7334
    @bastienp7334 Жыл бұрын

    Oh he is actually writing it all in mirror :)

  • @bastienp7334

    @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

    @ProfJeffreyChasnov

    Жыл бұрын

    @@bastienp7334 kzread.info/dash/bejne/iXaTpcOkoajSgZM.html

  • @bastienp7334

    @bastienp7334

    Жыл бұрын

    @@ProfJeffreyChasnov Hahaha thanks

  • @leewilliam3417
    @leewilliam34178 ай бұрын

    Mmmm😊

  • @abinayasivasamy4708
    @abinayasivasamy47088 ай бұрын

    Hope, am not the only person to suddenly see Jeff Bezos, and then realised.. Good teaching

  • @bravo803
    @bravo8033 жыл бұрын

    One Pen Man

  • @cowmata8492
    @cowmata84923 жыл бұрын

    GG

  • @nat.serrano
    @nat.serrano4 жыл бұрын

    why uTv becomes a 3,1 and uvT becomes a 3,3,...??

  • @RealLifeKyurem

    @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.

  • @ericklestrange6255
    @ericklestrange62554 жыл бұрын

    0 intuition, just formulas yet useful

  • @GarvitKhera185
    @GarvitKhera1855 жыл бұрын

    Are you left-handed or right-handed ?

  • @ProfJeffreyChasnov

    @ProfJeffreyChasnov

    5 жыл бұрын

    right

  • @OprichnikStyle

    @OprichnikStyle

    4 жыл бұрын

    too good to be true

  • @-long-

    @-long-

    4 жыл бұрын

    check this kzread.info/dash/bejne/qXeD19dpXdKbiaw.html

  • @benafrem
    @benafrem4 жыл бұрын

    Did anyone else mishear u2 as KZread 😂😂

  • @NikolaosLedZeppelin
    @NikolaosLedZeppelin Жыл бұрын

    how this guy writes that way ????!!!!

  • @pete4043
    @pete4043 Жыл бұрын

    wow, Jeff Bezos teaching math

  • @vanshajvidyan8458
    @vanshajvidyan84582 жыл бұрын

    Am I the only one who thinks he that he sounds like Yondu

  • @herbertwhite3665
    @herbertwhite36652 жыл бұрын

    how tf is this man writing this? he can write backwards??

  • @adamsterish
    @adamsterish4 жыл бұрын

    thank you jeff bezos

  • @blueice1364

    @blueice1364

    4 жыл бұрын

    I think all the white bald guys are named the same...

  • @ebramsaif3999
    @ebramsaif39992 жыл бұрын

    thanks