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词汇 Linear dependence
分类 英语词汇 英语翻译词典
释义

Linear dependence

原声例句
Linear algebra

So there your vector basics. And in the next video, I'll start getting into some pretty neat concepts surrounding vectors like span bases and linear dependence.

这就是矢量的基本知识 在下个视频中 我将开始讨论一些关于向量的非常简洁的概念比如张成的基底和线性相关。

中文百科

线性无关 Linear independence

(重定向自Linear dependence)

在线性代数里,矢量空间的一组元素中,若没有矢量可用有限个其他矢量的线性组合所表示,则称为线性无关线性独立linearly independent),反之称为线性相关linearly dependent)。例如在三维欧几里得空间R的三个矢量(1, 0, 0),(0, 1, 0)和(0, 0, 1)线性无关。但(2, 1, 1),(1, 0, 1)和(3, 1, 2)线性相关,因为第三个是前两个的和。

英语百科

Linear independence 线性无关

(重定向自Linear dependence)

The vectors in a set T=\{\vec v_1,\vec v_2,\dots,\vec v_n\} are said to be linearly independent if the equation

can only be satisfied by a_i=0 for i=1,\dots,n. This implies that no vector in the set can be represented as a linear combination of the remaining vectors in the set. In other words, a set of vectors is linearly independent if the only representations of 0 as a linear combination of its vectors is the trivial representation in which all the scalars ai are zero.

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