网站首页  英汉词典

请输入您要查询的英文单词：

　

单词 Dual vector
释义

Dual vector

原声例句
Linear algebra

Since both of these approaches give us a dual vector to the same transformation, they must be the same vector.

因为这两种方法都给出了同一个变换的对偶向量 所以它们一定是相同的向量。

Linear algebra

Then when we associate that transformation with its dual vector in three D space, that dual vector is going to be the cross product of V-N-W.

然后当我们把这个变换和它在三维空间中的对偶向量联系起来 这个对偶向量就是V-N-W的外积。

Linear algebra

But thinking geometrically, we can deduce that this dual vector must be perpendicular to VMW with a length equal to the area of the parallelogram spanned out by those two vectors.

但从几何角度考虑 我们可以推导出这个对偶向量必须垂直于VMW 其长度等于由这两个向量张成的平行四边形的面积。

Linear algebra

The takeaway is that whenever you're out in the mathematical wild and you find a linear transformation to the number line, you will be able to match it to some vector, which is called the dual vector of that transformation.

只要你在数学领域中找到一个到数轴上的线性变换 你就能将它与某个向量相匹配 这个向量被称为这个变换的对偶向量。

中文百科

线性泛函 Linear form

（重定向自Dual vector）

在线性代数中，线性泛函是指由矢量空间到对应纯量域的线性映射。在 \mathbb{R}^n ，若矢量空间的矢量以列矢量表示；线性泛函则会以行矢量表示，在矢量上的作用则为它们的矩阵积。一般地，如果 V 是域 k 上的矢量空间，线性泛函 f 是一个从 V 到 k 的函数，它有以下的线性特性：

f(\vec{v}+\vec{w}) = f(\vec{v})+f(\vec{w}) \quad \forall \ \vec{v}, \vec{w}\in V
f(a\vec{v}) = af(\vec{v}) \quad \forall\ \vec{v}\in V, a\in k

所有从 V 到 k 的线性泛函集合, 记为 \operatorname{Hom}_k(V,k), 本身即为一矢量空间，称为 V 的 (代数)对偶空间。

英语百科

Linear form 线性泛函

（重定向自Dual vector）
Geometric interpretation of a 1-form α as a stack of hyperplanes of constant value, each corresponding to those vectors that α maps to a given scalar value shown next to it along with the
Linear functionals (1-forms) α, β and their sum σ and vectors u, v, w, in 3d Euclidean space. The number of (1-form) hyperplanes intersected by a vector equals the inner product.[1]

In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars. In ℝ, if vectors are represented as column vectors, then linear functionals are represented as row vectors, and their action on vectors is given by the dot product, or the matrix product with the row vector on the left and the column vector on the right.  In general, if V is a vector space over a field k, then a linear functional f is a function from V to k that is linear:
随便看

　

英汉网英语在线翻译词典收录了3779314条英语词汇在线翻译词条，基本涵盖了全部常用英语词汇的中英文双语翻译及用法，是英语学习的有利工具。

　

Copyright © 2004-2024 encnc.com All Rights Reserved
更新时间：2025/6/27 2:35:09