This video explains why the dot product is about how much vectors point the same way.
Пікірлер: 257
@Improbabilities5 жыл бұрын
Just for the record, I do notice the effort you put into these videos. You're doing great! Keep it up!
@LookingGlassUniverse5 жыл бұрын
Thank you, that’s very very kind of you :)
@minandychoi85975 жыл бұрын
Looking Glass Universe yeah, please know it doesn’t go unnoticed by us!
@LookingGlassUniverse5 жыл бұрын
I really really appreciate that :)
@icyminglun51382 жыл бұрын
IM SO GRATEFUL FOR THESE textbooks arent doing much for me with numbers and formulas :') so thank you mam
@KHANPIN4 ай бұрын
Honestly, I wasn't expecting those pauses in the video, but turns out, they helped a lot with just grasping the concept and understanding. Thanks!
@FortniteMaster-vi6qt3 жыл бұрын
This is incredible, taking a concept that confused me to no end and helping me understand in 13 min. Thank you so much
@bijannatividad3 жыл бұрын
I've been looking at a lot of videos and forums looking for the practical meaning of a dot product. Every video and forum I found only defined what dot product is and they were very technical about it. This video gave me the answer after 5 seconds. Thank you!
@tejashreebhat1272 жыл бұрын
The amount of creativity in this video , the amount of efforts you have put in editing this. Salute. 🔥🔥
@shredda7 Жыл бұрын
literally the thumbnail alone explained it better than everyone else
@lucasfreitag97945 жыл бұрын
Finally a video on KZbin that gives a really intuitive visualisation of the dot product. Well done. Thank you.
@LookingGlassUniverse5 жыл бұрын
Thanks so much!!
@roger727153 жыл бұрын
Suddenly discovered this channel. Loving it!
@JohnWalz973 жыл бұрын
You're videos are amazing! Really helped me understand super daunting subjects. You're ability to break these topics down and explain them in a straightforward way is so awesome!!!
@sanjalisubash63072 жыл бұрын
Wow! I just started linear algebra and was already confused as to why dot products matter. The way you explain this is so good and you can really make out the effort in the videos. I can't believe I haven't seen your content before! Subbed right away!!
@aion21773 жыл бұрын
Wow. Finally i understand whats the point of the dot product. Should be called "similarity product" or something to point to it's meaning. Can't believe i went on all this years not understanding this basic idea.
@sanjaisrao484 Жыл бұрын
I cant even imagine how much work you did for this video , its great
@raphaelsisson30435 жыл бұрын
It's truly awesome (in every aspect) the videos you make. You don't need to feel bad about taking some time off. For me at least your videos are a gift and it is not fair with you that we demand anything. That's just my long way to say thank you!
@LookingGlassUniverse5 жыл бұрын
Thanks so much :D!
@Anna-qp1fi2 жыл бұрын
The first 8 seconds literally answered a question I've been trying to solve for the last 20 minutes with multiple websites and textbooks.
@no_360scope93 жыл бұрын
this is actually so sick, a lot of work went into this and it really did help me
@niranjanarunkshirsagar5 жыл бұрын
Amazing! Our human brain is evolved such a way that we understand anything very easily if it is intuitive & your techniques are so intuitive and gripping that anyone who is very weak in maths can learn by heart the very concept behind "dot product". In that way, your techniques can be called "compatible with evolution". Richard Feynman also had this ability. Go ahead!
@christophealexandre15385 жыл бұрын
We have been missing you! Every video you make is a little gem.
@LookingGlassUniverse5 жыл бұрын
Thank you so so much- that means the world to me.
@snehasishsaren8422 Жыл бұрын
How deeply you explained it!...OMG!...This is the only video in youtube I came across, to know more deeply dot product and it's significance...You are really doing great. 🌈
@pilotomeuepiculiares30175 жыл бұрын
WOW. This video is better than any classes I had in school or college. I'll watch again later and do the "youtube homeworks" in paper and not half-way in my mind. Thanks
@LookingGlassUniverse5 жыл бұрын
Thank you very much! Did you try the homeworks :)?
@skidogleb2 жыл бұрын
New favorite math channel! wow this was the style of explanation I've been searching for, such a helpful conceptual take.
@Grevil76 Жыл бұрын
Wow the production quality on this vid is crazy! Thank you for the great explanation too!
@Anna_Fortunka5 жыл бұрын
I know nothing about filming but this does look good! :) Also, it's so good to finally learn the meaning behind this formulas I've known for years. Thank you!
@LookingGlassUniverse5 жыл бұрын
Yay! Thanks for noticing the 1% (probably lower) increase in video quality.
@Anna-qp1fi2 жыл бұрын
Definitely subscribing! This is an amazing channel!!! Very well explained :)
@draganjonceski26394 жыл бұрын
finaly i understand the dot product i have been looking for this kind of an explanation for so long but only now i realy understand it thanks thanks thanks!!!
@openyourmind47083 жыл бұрын
This channel is actually amazing
@andresvalera14305 жыл бұрын
Yay i found another great math channel!, thank you very much now i can understand this not like those "explanations" that basically say the definition and the properties
@f1ctiАй бұрын
Outstanding explanation of the dot product! This is the first video-and I've seen plenty- that's helped me get an intuition for this concept. Thanks so much!
@RichardDownie795 жыл бұрын
I am madly in love with your voice!
@hadmeinthefirsthalfngl27173 жыл бұрын
Every comment section of every female youtuber ever. Very cliche way of simping.
@MrEiht5 жыл бұрын
While studying I listened to an old creepy prof. For hours and hours. And you run that down in less that 14 min AND with your sweet voice...thanks :)
@daviddeleon2925 жыл бұрын
Amazing videos. This really helped me understand the dot product.
@Camilacpinto3 жыл бұрын
Excellent video, and I loved the toothpast tip!
@acborgia13443 жыл бұрын
For Homework 2: If we take v_b as the unit vector on its axis, from the previous exercise we know that x = v_u . v_b / ||v_b|| and y = v_v . v_b / ||v_b|| Now we add v_u and v_v v_u + v_v = (x+y) * v_b + perp We apply the same theorem on x+y as on x and y (x+y) = (v_u + v_v) . v_b / [[v_b|| Now replace x and y by their expressions (the ||v_b||s cancel out) v_u . v_b + v_v . v_b = (v_u + v_v) . v_b (1) This shows the distributivity of the dot product (v_a * k) . (v_b . s) = ||v_a * k|| * ||v_b*s|| * cos(theta) = k * s * ||v_a|| * ||v_b|| * cos(theta) = k * s * v_a . v_s This shows the scalar multiplication property of the dot product (not sure if that's the right term lol) v_u = alpha * v_v1 v_v = beta * v_v2 Now we replace v_v and v_u in the formula (1) (alpha * v_v1 ) . v_b + (beta * v_v2) . v_b = (alpha * v_v1 + beta * v_v2) . v_b From last property this is the same as: alpha * v_v1 . v_b + beta * v_v2 . v_b = (alpha * v_v1 + beta * v_v2) . v_b This shows the dot product is bilinear Homework 2 finished
@harrytresor86545 жыл бұрын
Answer for the last question: So we have vectors a and b that can be written as a1x + a2y for vector a and b1x and b2y for b. Given the linearity formula for the dot product. a•b = (a1x + a2y)•(b) = a1x•b + a2y•b Substitute for b and we get: a1x•(b1x + b2y) + a2y•(b1x + b2y) a1x•b1x + a1x•b2y + a2y•b1x + a2y•b2y The dot products of orthogonal vectors is 0 so the equation simplifies to: a1x•b1x + a2y•b2y Since the are facing in the same directions, the is the same as multiplying their magnitudes together. Thus a•b = a1b1 + a2b2 ...
@LookingGlassUniverse5 жыл бұрын
Nicely done! Thanks for typing it all out :)
@usernameisamyth2 жыл бұрын
Ain't u gonna extend the playlist? I loved ur explanation.
@evasuser5 жыл бұрын
With gems like this we can partially forget or tolerate the crap that youtube is filled with. Thank you for the video and please keep making. How about PDEs or probability?
@thevideoride3 жыл бұрын
This video was awesome. A beautiful lecture that help the viewer better understand a confusing topic.
@BogdanTNT Жыл бұрын
Underrated video. Thank you
@ElPsyKongroo5 жыл бұрын
I totally forgot about this and we started using dot products for the first time since calc 3, thank you!
@LookingGlassUniverse5 жыл бұрын
Great!! So happy to help :)
@FF7EverCrisis3 ай бұрын
This is the best explanation to dot product. Thank u
@HamidKarimiDS2 жыл бұрын
Kudos! You are an amazing teacher! Well done. Keep up the good work.
@ironpatriot29052 жыл бұрын
وَحَدَّثَنَاهُ قُتَيْبَةُ بْنُ سَعِيدٍ، عَنْ مَالِكِ بْنِ أَنَسٍ، عَنْ أَبِي بَكْرِ بْنِ نَافِعٍ، عَنْ أَبِيهِ، عَنِ ابْنِ عُمَرَ، عَنِ النَّبِيِّ صلى الله عليه وسلم أَنَّهُ أَمَرَ بِإِحْفَاءِ الشَّوَارِبِ وَإِعْفَاءِ اللِّحْيَةِ . This hadith is in Sahih Muslim. Growing beard is a wajib act and not growing it is a sin.
@vasylarsenii48007 ай бұрын
Thank you so much! You're an extremely talented teacher.
@hashas69985 жыл бұрын
You're a great teacher.
@danielmccarthy4741 Жыл бұрын
Excellent video, thank you for your hard work.
@sajkdlsjf5 жыл бұрын
Excellent video and explanation. I applaud your efforts.
@roygreen82652 жыл бұрын
I cant tell exactly how gladful im after this point of view, i thought about it a lot and now thinga makes more sense!
@Psd8635 жыл бұрын
Yay, she's back!
@Sanjaybsnl083 жыл бұрын
It was a really nice one :) ,it actually gave me a clear picture of dot product
@gpamob5 жыл бұрын
Amazing. Thank you very very much.
@Sofialovesmath3 жыл бұрын
Amazing, you are incredible!
@mmoonchild27610 ай бұрын
May God bless you! This is beyond great.
@baqeralzaki923411 ай бұрын
I realised the depth of the info you share, not just the rules of it. I love it. Just a recommendation, I think it would be much better if it was less distracted. I wanted to focus on sth, but I just kept looking here and there on the necessary graphs, forgetting the point.
@sergiolucas38 Жыл бұрын
perfect didactic and editing, youre very talented :)
@rohitonam5130 Жыл бұрын
you are great....the animation is great, the moment trig enters DHAN TAN TAAAAA... i laughed very hard..😂😂😂😂 i'll never forget this for my life ,,,, I m very glad i watched it. thank you for this video, it explains very neatly and clearly the basic. I found exactly what i was looking for
@katiefaery3 жыл бұрын
So well explained. I appreciate it 🙂
@k-inquisitive90522 жыл бұрын
Are you a theoretical physicist
@dibakarbarman46625 жыл бұрын
this type of teaching is very good and very useful for beginners .
@LookingGlassUniverse5 жыл бұрын
Thanks very much!
@nnnn654905 жыл бұрын
Love the vid as always!!! : ) Will you do the cross product too? I actually don't know why it works...
@LookingGlassUniverse5 жыл бұрын
Thank you! I wasn’t planning to, since 1)I don’t know the answer (though it could be fun to figure it out) 2) the cross product doesn’t generalise nicely like the dot product. Sorry!!
@natasadjurdjevic35335 жыл бұрын
You deserve more views
@breadyogurt39572 жыл бұрын
Can we reboot the series, starting with the cross product? 👀
@kaushikgupta94905 жыл бұрын
Awesome video !
@LookingGlassUniverse5 жыл бұрын
Thank you!!
@colorx6030 Жыл бұрын
Holy crap I just wanted to understand dot product for my Physics class but I somehow ended up in Linear Algebra.
@kirancp4758 Жыл бұрын
This is the best intuitive explanation for the dot product .Can you please do the same for cross product
@lightyagami-rk2my2 жыл бұрын
Thanks for this video. I searched for this
@555620092 ай бұрын
dot product between one orthonormal basis vector with itself comes out to be 1 because 1*1*cos 0 =1 and with any other orthonormal basis vector it becomes 0 because they are orthogonal i.e. cos 90. Therefore we get the neat formula to multiply corresponding coordinates to get dot product between 2 vectors. Thanks I really had that doubt why this formula works.
@wavelet48665 жыл бұрын
YaY you are back!!
@LookingGlassUniverse5 жыл бұрын
Sorry for disappearing!
@jeroenw98535 жыл бұрын
I never knew I had all these problems. But luckily I can solve (most) of them! 🧠
@Steve-mo4qp3 жыл бұрын
This is great.
@anegativecoconut49405 жыл бұрын
3:35 No God! No God Please no. No! NO! NOOOOO!
@swojnowski4533 жыл бұрын
put a hat on the vectors so that you don't have to remember you have made them unit vectors ;)
@swojnowski4533 жыл бұрын
Well done.
@Thror2515 жыл бұрын
Is it usual to write the dot product with the dot at the bottom? Everyone I know always writes it with the dot in the center (in LateX this would be \cdot).
@duckymomo79355 жыл бұрын
Thror251 There’s many ways Some write it like this
@LookingGlassUniverse5 жыл бұрын
@Mi Les yup :) I write it down because I use \cdot for multiplication sometimes. But it doesn't matter too much!
@michaelsommers23565 жыл бұрын
@@duckymomo7935 Or .
@michaelsommers23565 жыл бұрын
@@LookingGlassUniverse I use \bdot for the dot product, but I also use bold symbols for vectors. I define it as: \usepackage{amsmath} ewcommand{\bdot}{\boldsymbol\cdot} and for the cross product ewcommand{\cross}{\boldsymbol\times}
@LookingGlassUniverse5 жыл бұрын
Oh, that’s a nice way to do it!
@blblbl27505 жыл бұрын
really nice video !
@LookingGlassUniverse5 жыл бұрын
Thank you!
@henrycraft95413 жыл бұрын
Yes, an identical unit vector in the opposite direction should be minus. (And this means the dot product has to be Zero). I think I get it! I really like your question, to what extent are the two vectors going the same way.
@rosuav5 жыл бұрын
6:10 Awwww, I like your toothpick vectors!
@LookingGlassUniverse5 жыл бұрын
Haha! At least there’s one.
@thevegg32752 жыл бұрын
Great video but I have a question. I like how using unit vectors creates a range of -1 to 1 when rotating one of the two parallel vectors wrt the other. But if the lengths of the two parallel vectors is 5, then the range is -25 to 25. Using your definition of the dot product gives "The dot product shows how much of a vector is in the direction of the other. Therefore 5i dotted with 5i...500% of one vector is in the direction of the other vector. Does that sound a little odd? Thanks!
@dolanfragrance22743 жыл бұрын
wth this video is so good
@ittooklongtomakethis5 жыл бұрын
lol the toothpick thing is relatable. I use chalk to represent a 3d vector on a chalkboard sometimes :D
@LookingGlassUniverse5 жыл бұрын
Haha! Do you teach vectors?
@b0606089 Жыл бұрын
The animations 😍
@timsmith90732 жыл бұрын
You are awesome...or at least your videos are!
@jeevanandam.exll-a88672 жыл бұрын
Yeah I take some time to get that it is cos but where did you get this concept ,
@benharris76015 жыл бұрын
Thanks for not explaining homework one now I have no clue how to do the rest
@pennyl87732 жыл бұрын
For 8:09, if x = u cos theta, then why isn't y = u sin theta? For u.v2 , wouldn't the angle be 90 - theta? Thanks.
@muratcan__225 жыл бұрын
Perfect
@kirkhamandy5 жыл бұрын
Nice video, curl next?
@dibakarbarman46625 жыл бұрын
please mam make some videos about Isospin ,Hyperchage (particle physics)
@77kiki77 Жыл бұрын
Why don't you write 1/√2 as (√2)/2 ? It's easier to understand, and more flagrant with the remarkable trigonometric value than just 1/√2. Though I appreciated this video, twas really helpful, 'cuz it's not ony about understanding the formulas and applying these, it's also about understanding what does it mean. Thanks to you, I did
@Hecatonicosachoron5 жыл бұрын
Doesn't almost organic solvent you buy at the chemist's work for wiping off the marker from the white board?
@LookingGlassUniverse5 жыл бұрын
I was using whiteboard cleaner and it ruined my board. Now nothing but toothpaste really works. It’s really ugly in real life, but I just put the contrast on high so you don’t see it
@MidnighterClub5 жыл бұрын
OK here's a weird thought. As you draw a vector in various positions around a circle, I notice that the dot product is not unique. 0 (zero) occurs twice as the vector rotates in a circle, once at 90 degrees and once at 270 degrees. But the vector is in different positions!! So are there different zeros here? Is zero not always equal to zero? It seems like there should be some way to distinguish between those different positions.
@ejetzer5 жыл бұрын
Gojira There are, but not with the dot product. We go from two vectors of two or more dimensions, to a single real number, so some information gets lost: we can’t distinguish between an angle and its full circle complement, or between acute and obtuse angles, or between negative and positive angles. The dot products tells us how much the vectors point in the same way, but not where they initially pointed.
@LookingGlassUniverse5 жыл бұрын
Really nice observation/ question, and great answer. That’s exactly right, the dot product doesn’t uniquely determine where the other vector is relative to the first. Come to think of it, that’s why when you want to specify a vector wrt a orthonormal basis, you need specify the dot product of it with every basis vector
@mesutkaraman96774 жыл бұрын
To handle with nonuniqueness, assuming all the vectors are in the same quadrant may help. Just a triggered thougt, why nonnegativity is so important for recommendation systems. Since all components have positive value, comparing two client's rankings by using dot product is a well suited approach.
@LeenaBora4 жыл бұрын
Hi. The video started with: We want some way to describe - how much 2 vectors are pointed in same direction? And answer is dot products helps in achieving that. But why can't we use simply angle between 2 vectors for the same thing. (I am not talking about cos(theta) ) simply angle. Reason why we can't use angle in this case is, it will work in 2D but not in higher dimension. So we need some other way to describe it. Is this geometrically correct statement?
@mbappekawani97163 жыл бұрын
the reason the dot product increases the more similar two vectors are and is smaller the less similar they are is because: 1. you can breakup each vector into the same basis components that can have opposite magnitude pieces of each other when two vectors point in different directions. 2. those negatives cancel out a lot in the calculation with the positives
@dragonlovesdiamond95122 ай бұрын
I have a question, isn’t the dot product also used for how much two vectors are alligned? How can the formula also use this definition and how much these are pointing the same way
@DistortedV125 жыл бұрын
Mithuna WE LOVE YOU!
@sharanya20454 жыл бұрын
For the proof of the linearity of the dot product, isn't it kind of obvious if we are multiplying scalars?
@zarchy555 жыл бұрын
If the dot product of two vectors can be thought of as a measure of how much the two vectors are pointing in the same direction, would there be any significance to generalizing this idea to n vectors?
@LookingGlassUniverse5 жыл бұрын
I’ve never seen such a thing, but maybe you could? You can at least certainly generalise the dot product for n dimensional vectors, but that’s not the same thing. So yeah, I don’t have a great answer, sorry!
@goSomewhereElse3 жыл бұрын
This is really great, once in a while I look at a dot product and I'm like "why the heck sr cos() again?"
@vinayakpendse72335 жыл бұрын
I just watched is spinning angular momentum video, When particle does larmor precession why don't its angular momentum go on increasing?
@LookingGlassUniverse5 жыл бұрын
I don’t know, what do you mean?
@ApplepieFTW4 жыл бұрын
9:40 hold on how does this make sense at all. we know that a•b is the part of a in the direction of b, right? so it's a bit like, where the projection of a on b is, that's the vector a, minus the "orthogonal to b" bit. so why does the length of b matter? if I make b very large, and have a stay the same, wouldn't the projection land in the same spot? and if I make a really big, wouldn't it then land on a different spot instead? and also, why is it logical at all that you have to devide by the length of b? since, how exactly does its length change the projection?
@avanishpadmakar58975 жыл бұрын
Let vector be represented as |a> Then each vector can be represnted as a matrix of the order N×1 where N is number of basis vectors and each number in the matrix will follow a(j1)=|a>•|v(j)> where 1 is smaller than or equal to j is smaller than or equal to N The matrix for product formula follows. And due to linearity property |a>•|b>=a1• (b1+b2....bN)+ a2• (b1....bN)..aN• (b1..bN) As ai is orthonormal to bj for i not equal to j so 0 for i not equal to j ai•bj ={ } |ai||bj| for i=j Hence |a>•|b>=sigma (|ai||bi|) where i varies from 1 to N
@abdullahalmasri6125 жыл бұрын
Wait so after learning more about linear algebra i figured out that vectors can also be like...functions or any things that satisfies the 8 linearity axioms So what about when vectors aren't "arrows"?
@LookingGlassUniverse5 жыл бұрын
That’s the next video :)! But what in particular would you like to know? I can try include it in that video
@abdullahalmasri6125 жыл бұрын
@@LookingGlassUniverse tbh anything is good, because i don't know what i don't know so i can't say what i want in the next vid And anything i know is also good because it might strength my understanding on the thing or fix it if i was understanding wrong :)
@Basaltq3 жыл бұрын
What poll? I can't see any poll.
@rosuav5 жыл бұрын
12:37 Inquiring minds must know: what colour were the roses?
@LookingGlassUniverse5 жыл бұрын
White but splattered with red paint for some reason...