Expressing a quadratic form with a matrix

Nice job !

Beautifully explained. My notes make sense now.

Then you are the same guy of 3B1B😃

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

Super clear. Thanks!

it is very nice

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!

Let me put my hands on your kneees Angelina Jolie

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.

thanks, winning chess niow

I just realize this is Grant Sanderson's voice

Our hero

Great video. Thanks for the help

Ok am I crazy or is this 3Blue1Brown talking?

reis

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

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

Why is Grant Sanderson on Khan Academy!

I wish they would link the next video in the description

I love you man from 3blue1brown

Is that the voice of 3b1b?

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

Any Indians 🇮🇳

omg is there anything you don't know?

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

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

Thank you so much Sir.../\

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

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

love u 3blue1brown

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

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

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

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!

Wow this really helped for exams

I thought I was watch 3b1b for a sec

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

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

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

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

OMG YESSSSSSSSSS 3BLUE1BROWN!!!!!

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

SK and this guy are absolutely my favourite online educators

Where is the next video of this series?

Thank you sir !

Why is 3Blue1Brown there?

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

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.