![Keenan Crane on Twitter: "[26/n] More precisely: The *gradient* is the vector whose _inner product_ with any vector X gives the directional derivative along X. So: a different inner product gives a Keenan Crane on Twitter: "[26/n] More precisely: The *gradient* is the vector whose _inner product_ with any vector X gives the directional derivative along X. So: a different inner product gives a](https://pbs.twimg.com/media/E70XQzPWQAICKGO.jpg:large)
Keenan Crane on Twitter: "[26/n] More precisely: The *gradient* is the vector whose _inner product_ with any vector X gives the directional derivative along X. So: a different inner product gives a
![SOLVED: Let V = P(R), equipped with the inner product defined by (f,g) = ∫[a,b] f(t)g(t) dt. Then 12v₠- 3v₂ + 2v₃ is an orthonormal basis for V. (You do not SOLVED: Let V = P(R), equipped with the inner product defined by (f,g) = ∫[a,b] f(t)g(t) dt. Then 12v₠- 3v₂ + 2v₃ is an orthonormal basis for V. (You do not](https://cdn.numerade.com/ask_images/0e9ea490a6134442953bb7305b5c7a2a.jpg)
SOLVED: Let V = P(R), equipped with the inner product defined by (f,g) = ∫[a,b] f(t)g(t) dt. Then 12v₠- 3v₂ + 2v₃ is an orthonormal basis for V. (You do not
![real analysis - About the definition of functional derivative and the $L^2$ inner product - Mathematics Stack Exchange real analysis - About the definition of functional derivative and the $L^2$ inner product - Mathematics Stack Exchange](https://i.stack.imgur.com/quIZo.png)
real analysis - About the definition of functional derivative and the $L^2$ inner product - Mathematics Stack Exchange
![differential geometry - Differentiating the inner product of two vector fields in terms of covariant derivatives - Mathematics Stack Exchange differential geometry - Differentiating the inner product of two vector fields in terms of covariant derivatives - Mathematics Stack Exchange](https://i.stack.imgur.com/AlI0z.png)