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单词 Linearly dependent vectors
释义

Linearly dependent vectors

原声例句
Linear algebra

It means that the linear transformation squishes all of two d space on to the line where those two vectors sit, also known as the one dimensional span of those two linearly dependent vectors.

它意味着线性变换将所有二维空间压缩到这两个向量所在的直线上 也称为这两个线性相关向量的一维张成的空间。

中文百科

线性无关 Linear independence

(重定向自Linearly dependent vectors)

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Linearly dependent vectors)

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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更新时间:2025/6/22 4:48:25