Expressing a quadratic form with a matrix

[@willwonkers]

Exam tomorrow, somehow hearing Grant's voice was all I needed right now.

[@xanderalaric228]

sorry to be so offtopic but does any of you know a trick to log back into an Instagram account?? I somehow forgot the login password. I would love any assistance you can offer me.

[@mathiasjayson676]

@Xander Alaric Instablaster :)

[@YuqiChen-s5n]

The greatest to ever do it.

[@falcz]

If all the teachers in the world had the ability to explain things like Grant Sanderson, we would have already become a galactic civilization for decades.

[@joshdominguez2765]

I knew this soothing voice was so familiar. The calming voice that brings you peace when sailing through the raging storms of calculus and linear algebra. 3Blue1Brown!

[@picknikbasket]

"more intimidating than it needs to be" Love it!

[@Mirandorl]

SK and this guy are absolutely my favourite online educators

[@mayue6195]

is he 3Blue1Brown?

[@ValyPCM]

yes, he is

[@Originalimoc]

Sounds really like. And yes. He's on Khan academy.

[@gimmemoreborisbrejcha9794]

@@Originalimoc He was.

[@adityaroshan1688]

Yes he is grant Sanderson

[@billycheung5114]

He not a human

[@ben_hkw117]

Viusal learning is always better than reading plain text. Nice video!! Need more of this. Gracias!!

[@mltyblnd]

grants voice makes me so happy

[@sgracem2863]

I wish they would link the next video in the description

[@berknevzat7995]

I never thought I could pass the exam but now, I know I will

[@samirkhan6195]

Its called quadratic form because this part decides the form(nature) of the curve , based upon the values of a,b,c alone one can determine whether the curve is circle,ellipse,parabola or hyperbola... other linear terms like dx+ey and costant term f gives control over additional customisations to the curve...

[@Dezomm]

Love these videos. Thank you so much for helping people learn this stuff!

[@Tsoenyana]

What software do you use for videos and writing?

[@xixi1770]

how can i find the playlist of this video? or what's the whole series that contain this video??

[@RebekahParkhurst]

I can't find the next video after this. It's not in a playlist and youtube doesn't show me which one comes next. I'd like to find the next video please!

[@viggobertrand3067]

Beautifully explained. My notes make sense now.

[@acuriousmind7458]

3 blue 1 brown guy :D

[@hyunwoopark9241]

I was just looking for any vids for my test tomorrow and walla!! 3B1B appeared!

[@julesthomas3335]

Why do we use a 1 by n matrix instead of take the dot product ?

[@yongjaecho6039]

I've found this theory all day... thank you :)

[@EvilDudeLOL]

"Pause the video, go find a matrix multiplication video and kimda refresh about that." Oh boy have I got a channel for you

[@ZIMINYANG-e5d]

i did not expect threeblueonebrown!

[@douglasespindola5185]

Ok, and how could I write a common function like f(x) = x^2 + 3x + 5 in a matrix form? Should I split it in two vectors like A = [ 1, 3, 5 ] times [ x^2, x, 1] ? If don't, what am I missing? Thanks.

[@ryanjackson0x]

You would still do x^T*M*x and determine M as he does in the video. The vector input to M will have the second value constrained to be 1. The reason is that f(x) yields a single value, and M yields a vector -- they are not equivalent as-is.

[@aeroscience9834]

0:55 wrong. It's called a quadratic form because in abstract linear algebra, it comes from something else called a bilinear form, which is a type of map involving vector spaces en.m.wikipedia.org/wiki/Bilinear_form

[@Skankhunt-xr5lb]

Aeroscience you must be fun at parties

[@tranhuy4713]

+Skankhunt42 if he is invited to one

[@Hlkpf]

Started the video; originally just wanted to confirm that it was what I thought it was "i know that voice" and then i watched it all :-D what kind of sucker am I xD

[@martingutlbauer9071]

Is there a way to epand this to higher derivatives like 3rd or 4th derivatives? How would a "cubic form" look like?

[@nathanielsaxe3049]

yup, if you want to use 3rd derivatives you need a 3 dimensional Hessian matrix which contains things like (partial^3 f) / (partial x^2 partial y), 4th derivatives need a 4 dimensional Hessian etc.

[@qltcn]

There is actually a book on Cubic forms by russian mathematician Yuri Manin.

[@MrVaskor]

A helpful video - thank you. I am currently working on an efficient way to compute the quadratic form result x^T M x where x and M are given (or at least can be computed based on given rules) but x is a massive vector with 1,048,576 elements and M is a massive 1,048,576x1,048,576 matrix, so multiplying everything out would take forever. I think I have an idea on how to do it, since I believe the rules given allow a shortcut, which I now need to implement. Once I have finished that, I have a task of repeating the process for an even bigger x vector with 1,073,741,824 elements and an M matrix with 1,073,741,824x1,073,741,824 or around 1.15 quintillion elements!

[@crashbunks]

But why?

[@MrVaskor]

@@crashbunks For the IBM Research Ponder This May 2023 puzzle

[@Elvis0]

gl

[@bryanDaMazo16]

How can you multiply 2x1 and 2x1 matrix? shouldn't it be transpose of first one, then 1x2 and 2x1?

[@aleksandrbakhmach9810]

Nice job !

[@_NEO__]

Wow this really helped for exams

[@ronindeschamps2993]

Can someone explain why he mulitplies the matrices right to left rather then left to right. This is especially confusing becuase matrix multiplication is not commutative and is normally done left to right.

[@brightsideofmaths]

Really nice :)

[@yz1561]

Super clear. Thanks!

[@tomaswust3505]

Great video. Thanks for the help

[@aram69420]

I just realize this is Grant Sanderson's voice

[@HuefulPhoenix]

Our hero

[@Enlightenchannel]

Why is Grant Sanderson on Khan Academy!

[@souravkarmaker4534]

Thank you sir !

[@godfreybaiga3804]

Great explanation keep up dear

[@gregorymacchio4077]

OMG YESSSSSSSSSS 3BLUE1BROWN!!!!!

[@silvestersourn4125]

How do I do a quadratic Formula with no X squared??

[@vf5400]

Thank you!!

[@ferdowsalom2249]

Then you are the same guy of 3B1B😃

[@mevadeva1397]

i think it's called a quadratic form instead of "pure quadratic equation" because of similarities with linear algebra, where that second term would be nonsensical and unnecessary long

[@360wheelz5]

Plot twist: Grant working part-time at Sal's.

[@dominicj7977]

He was an intern

[@thabangmasetloa4534]

Thank you

[@emlmm88]

Weird that we didn't cover this until Linear Algebra.

[@JalRuotGatkuoth]

it is very nice

[@vainonurmi4052]

Where is the next video of this series?

[@TheAcujlGamer]

looking into it too

[@TheAcujlGamer]

www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/quadratic-approximations/v/vector-form-of-multivariable-quadratic-approximation

[@cola175]

.."more intimidating than it needs to be" . Exactly the thing I always hated!

[@MultiJman01]

Why multiply with x transposed and not just take the dot product?

[@EvsEntps]

You can, but you would have to put brackets around the matrix and the x-y vector to emphasise the order of operation, because you can't dot product a vector with 2x2 matrix.

[@ryanjackson0x]

Dot product isn't good enough for this purpose because in the dot product operation, the unknowns (x, y, etc.) fall away from the result, and in this case, we need them to find the quadratic form.

[@studiant3004]

I love you man from 3blue1brown

[@benkim6969]

0:58

[@DistortedV12]

Why is 3Blue1Brown there?

[@niravgujarathi2296]

what exactly is the purpose of the symmetric matrix... Couldn't you generate a quadratic form even without a symmetric matrix?

[@rinzhler6922]

3:19 - 3:29

[@niravgujarathi5502]

@@rinzhler6922 thanks a lot 👍👍

[@rinzhler6922]

@@niravgujarathi5502 👍

[@edslab5383]

Is that the voice of 3b1b?

[@thalescosta7602]

3b1b?

[@lordleoo]

i've been searching for something related to this, for hours, and can't find a clue. the algebra we studied in school is for scalars, you deal with stuff like ax^2 and x/a or x/a and so on. now with matrices, if instead of a scalar, you have a sequence of scalars, and you want to represent ax^2 for each one of them, you write transpose(a) * x * a if you want to represent [ax, by, cz] you write: diag([a,b,c]) * [x,y,z] where can i find a list of such relations? how to convert equations/functions from scalar form to matrix/vector representation. i've been looking for hours. i want a list of those relations, or the name of this field.

[@RishikavsAnnie]

This doesn't seem to work with real matrices of order 3 (Converting a matrix into a quadratic expression).

[@vaishnavchandra5220]

......................Grant Sanderson

[@srinityapadma5125]

Thank you so much Sir.../\

[@universe-ity9029]

Does "form" seem that fancy? Sounded pretty plain to me.

[@sssilky3317]

Ok am I crazy or is this 3Blue1Brown talking?

[@harrywang6792]

I thought I was watch 3b1b for a sec

[@ashwaqahmed4890]

He is

[@user-hx6qy3ev9x]

love u 3blue1brown

[@wiz9858]

thanks, winning chess niow

[@bunnietzui6593]

omg is there anything you don't know?

[@TimePass-lk7pm]

Any Indians 🇮🇳

[@studiant3004]

Yeah, I'm not indian but I totally dont have nothing against you haha

[@zsaruar]

😍

[@kaandesu4881]

reis

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[@changqu612]

sound like you said the "n" word at the beginning, lol

[@alial-musawi9898]

Chang Qu I always hear this word when chinese people say 那个