Timeline for Why is gradient a vector?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2022 at 23:34 | answer | added | FeedbackLooper | timeline score: 3 | |
| Feb 14, 2022 at 21:23 | answer | added | TurlocTheRed | timeline score: 1 | |
| S Feb 14, 2022 at 20:17 | history | suggested | Dan Doe | CC BY-SA 4.0 |
Use Mathjax
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| Feb 14, 2022 at 20:06 | review | Suggested edits | |||
| S Feb 14, 2022 at 20:17 | |||||
| Feb 14, 2022 at 19:46 | comment | added | William M. | Differentiability means linear approximation at a point. The "gradient" is the vector representation of the linear transformation in this approximation. There are some geometrical motivations that makes the gradient to be thought as a "direction of maximal increase" (this is a good intuition, albeit not a mathematical theorem). This is the direction you were missing. | |
| Feb 14, 2022 at 19:26 | answer | added | Cathartic Encephalopathy | timeline score: 6 | |
| Feb 14, 2022 at 19:11 | answer | added | Seub | timeline score: 1 | |
| Feb 14, 2022 at 19:10 | comment | added | Chessnerd321 | The basic idea is that the length/norm of the gradient is the maximum rate of change of $z(x,y)$ at the point $(x,y)$. It also turns out that the direction of the maximum rate of change is also the direction in which the gradient points. For those two reasons, it is nice to think of the gradient as a vector. Then plotting the gradient of a scalar function as a vector field shows which direction is "uphill". | |
| Feb 14, 2022 at 19:05 | history | edited | DDG | CC BY-SA 4.0 |
added 62 characters in body
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| S Feb 14, 2022 at 18:59 | review | First questions | |||
| Feb 14, 2022 at 19:00 | |||||
| S Feb 14, 2022 at 18:59 | history | asked | DDG | CC BY-SA 4.0 |