梯度

Also known as gradient of a scalar function, gradient operator, grad, grad operator, gradient vector

多元导数的泛化

AI overview

A gradient is a mathematical tool that shows which direction a quantity is changing most steeply at any given point, like how a slope indicates the steepest way up a hill. It matters because it helps scientists and engineers understand how things like temperature, pressure, or other quantities vary across space, which is essential for solving real-world problems.

AI-generated from the Wikipedia summary — may contain errors.

In the Vinony graph

Vinony's link graph records 994 inbound references to 梯度, and connects out to differential, calculus and integral.

Vinony files it under Differential calculus, Differential operators and Generalizations of the derivative.

Vinony links it to 65 Wikipedia language editions.

Wikidata facts

Instance of: mathematical expression

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different from: nabla operator
notation: ∇
Commons category: Gradient fields
maintained by WikiProject: WikiProject Mathematics

Sources (1)

wikidata.org

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Article · 中文

在向量微积分中，梯度（英語：gradient）是一种关于多元导数的概括。平常的一元（单变量）函数的导数是标量值函数，而多元函数的梯度是向量值函数。多元可微函数在点上的梯度，是以在上的偏导数为分量的向量。就像一元函数的导数表示这个函数图形的切线的斜率，如果多元函数在点上的梯度不是零向量，則它的方向是这个函数在上最大增长的方向、而它的量是在这个方向上的增长率。梯度向量中的幅值和方向是与坐标的选择无关的独立量。在欧几里德空间或更一般的流形之间的多元可微映射的向量值函数的梯度推广是雅可比矩阵。在巴拿赫空间之间的函数的进一步推广是。

Abstract from DBpedia / Wikipedia · CC BY-SA