The Hessian matrix | Multivariable calculus | Khan Academy

The Hessian matrix is a way of organizing all the second partial derivative information of a multivariable function.

[francescomura]

if anyone is wondering why the mixed derivates are the same: it's Schwarz's theorem.

[balajilakshminarayan]

Grant <3. Always helping me with math

[therealbean]

Hey Grant, Love your video's from Khan and 3Blue1Brown!

[AJ-etvf]

Awesome video! Thank you! And wow! It's 3Blue1Brown's voice doing this video!

[haiarpyzargarian]

Thank you so much, here I get much more infornation in one day than in university in a month)))

[shcraft.]

You have the same voice as the guy on 3blue1brown

[catouncormery]

you are perfect, thanks for you videos, and you're fanny mood :)

[jasonsoto]

Yo Khan Academy, thank you for making these videos. They are a real lifesaves at times ^w^

[MohamedJama-zttk]

I love u Khan!! u save me today
<333 very

[anamitrasingha]

So is this Hessian matrix is valid only for scalar valued functions right? If my intuition is correct then for a vector valued function of maybe 4 components, would there be 4 Hessian matrices?

[subashsubashsubash]

Thank you sir, this video has given me a good idea

[im-alida]

awesome! :-)
i have a question
what kind of tools are you using when you work??

I really wanna get that blackboard tool :-) thx in advance

[debralegorreta]

What does the Hessian matrix represent geometrically? In particular, what does the determinant of the Hessian matrix measure?

[hussainbhavnagarwala]

what if the output of function f was a vector of 3 rows instead of a single expression. How would the hessian change?

[siyuzhang]

the moment I clicked on this link, oh this is the 3blue1brown guy!

[BayesianBrain]

Can someone explain why the ideal learning rate for 2 or more dimensions in the gradient descent algorithm is the inverse of the Hessian (matrix of second partial derivatives)?

[rubyemes]

Sal, if I have 1 equation and 6 independent variables, my partial first derivatives is a vector with 6 terms. If I follow, the Hessian will be a 6x6 matrix. Is that correct? Thanks!!! I contribute to you as your program and platform makes an amazing contribution!

[vsprwlz]

how do i know which channel of khan academy is for this video?

[wunanzeng]

Do you guys know which lecture/series/playlist is this video from? Please let me know! Thanks!

[shantanu_bhattacharya]

Good day, I was wondering whether you know any python library that has implemented second order gradient descent with hessian error matrix. If you can point me to the right direction, it would be very helpful. Thanks in advance, Kind regards
Shantanu