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

$igtriangledown _xf(x) = Ax + b$

and

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

Is this just a issue of acquisition a derivative v respect to X, how would you attack this one?


*

*

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

You are watching: What does an upside down triangle mean in math

On the other hand, $ abla^2 f$ appears to be used here in an unusual way, namely to denote the Hessian (the matrix of all second 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 because that contributing solution to keolistravelservices.com Stack Exchange!

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

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based upon opinion; earlier them up with references or personal experience.

Use keolistravelservices.comJax to style equations. keolistravelservices.comJax reference.

See more: Battle Creek & Kalamazoo Insurance Companies In Battle Creek Michigan

To learn more, check out our advice on writing great answers.


write-up Your answer Discard

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


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


*

site design / logo design © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.5.40661


keolistravelservices.comematics stack Exchange works finest with JavaScript allowed
*

her privacy

By clicking “Accept all cookies”, you agree ridge Exchange have the right to store cookie on your an equipment and disclose info in accordance through our Cookie Policy.