Expressing a quadratic form with a matrix

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How to write an expression like ax^2 + bxy + cy^2 using matrices and vectors.
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Exam tomorrow, somehow hearing Grant's voice was all I needed right now.

willwonkers
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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!

joshdominguez
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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.

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

picknikbasket
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SK and this guy are absolutely my favourite online educators

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

ben_hkw
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I wish they would link the next video in the description

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

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

Dezomm
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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...

samirkhan
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Beautifully explained. My notes make sense now.

viggobertrand
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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!

RebekahParkhurst
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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!

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

hyunwoopark
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What software do you use for videos and writing?

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

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

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

julesthomas
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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

Hlkpf
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"Pause the video, go find a matrix multiplication video and kimda refresh about that."

Oh boy have I got a channel for you

EvilDudeLOL