Wouldn't there be the gradient more suitable notation instead of the Jacobian for the case f: R^n -> R? Jacobians are the general case for R^n -> R^m, but a bit too general for the function you are describing I think.
As we have seen in part 8, gradient and Jacobian carry exactly the same information in this case. Still the Jacobian is better here because otherwise you have to write an inner product with the gradient ;)
@brightsideofmaths True, I have to admit I did not watch your full series, just came here to understand multivariate taylor expansion more clearly. Good explanation btw! Of course it is fine, I just did not see this variant of notation in any of my lectures. They do a different trade off, and choose to write (x-a)^T * gradient to indicate the dimensions clearly, instead of uniformly using a Jacobian that could have any dimension. You would have to do some mul-add operation either way, I don't quite see that as an argument for it to be "better". Still, if you decided that early on I understand why. :)
![Multivariable Calculus 17 | Taylor's Theorem - Examples [dark version]](http://i.ytimg.com/vi/0gADi9YZG_A/mqdefault.jpg)
![Multivariable Calculus 17 | Taylor's Theorem - Examples [dark version]](/img/tr.png)
Can't wait to get to the Lagrange Multipliers :)
Hi, Is there any material showing how the quadratic approximation formula is derived?
My Real Analysis course could help there :)
Wouldn't there be the gradient more suitable notation instead of the Jacobian for the case f: R^n -> R? Jacobians are the general case for R^n -> R^m, but a bit too general for the function you are describing I think.
As we have seen in part 8, gradient and Jacobian carry exactly the same information in this case. Still the Jacobian is better here because otherwise you have to write an inner product with the gradient ;)
@brightsideofmaths True, I have to admit I did not watch your full series, just came here to understand multivariate taylor expansion more clearly. Good explanation btw!
Of course it is fine, I just did not see this variant of notation in any of my lectures.
They do a different trade off, and choose to write (x-a)^T * gradient to indicate the dimensions clearly, instead of uniformly using a Jacobian that could have any dimension. You would have to do some mul-add operation either way, I don't quite see that as an argument for it to be "better".
Still, if you decided that early on I understand why. :)
Thanks! Okay "better" is maybe an overstatement but I just like it more with the Jacobian :D Tehn I just don't need to write ^T@@chrystalkey9907
And I would recommend to watch the whole series to get a full understanding :)
waste of time
For me or for you? xD
some people are just bitter, huh.