where A is an nxn symmetric matrix, b is an n-dimensional vector, and alpha a scalar. Display that

$igtriangledown _xf(x) = Ax + b$

and

$H = igtriangledown ^2_xf(x) = A$

Is this simply a issue of taking a derivative with respect come X, exactly how would you attack this one?


*

*

$ abla f = (partial f/partial x_1, ldots, partial f/partial x_n)^t$ denotes the vector that partial derivatives that $f$ and is a completely standard notation.

You are watching: What does the triangle mean in physics

On the other hand, $ abla^2 f$ appears to be used right here in an unusual way, namely to denote the Hessian (the matrix of all 2nd order partial derivatives), $(partial^2 f/partial x_i partial x_j)_i,j=1^n$.

(The usual an interpretation of $ abla^2 f$ is the Laplacian, $partial^2 f/partial x_1^2 + ldots + partial^2 f/partial x_n^2$.)


*

Thanks for contributing an answer to bsci-ch.orgematics Stack Exchange!

Please be sure to answer the question. Administer details and share your research!

But avoid

Asking because that help, clarification, or responding to other answers.Making statements based upon opinion; back them increase with referrals or an individual experience.

Use bsci-ch.orgJax to format equations. bsci-ch.orgJax reference.

See more: 120 Out Of 150 Is What Grade, What Is A 150 Out Of 200 Grade

To discover more, see our advice on writing great answers.


post Your prize Discard

By click “Post your Answer”, girlfriend agree come our regards to service, privacy policy and also cookie plan


Not the prize you're spring for? Browse various other questions tagged linear-algebra notation or ask your very own question.


*

site design / logo © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.22.40552


bsci-ch.orgematics stack Exchange works ideal with JavaScript enabled
*

your privacy

By clicking “Accept every cookies”, girlfriend agree stack Exchange have the right to store cookies on your device and disclose details in accordance with our Cookie Policy.