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1.The dot product imprinted burliness, overprinter quasi-three, restore, see double streak-free.

1.这些产物痕迹准、无条痕、无轻影。

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玩转物理学

1.However, let's use E dA cosine theta instead of the dot product.

我们使用 E dA 余弦西塔来代替机翻

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玩转物理学

2.Electric flux equals the integral of the dot product of electric field and dA.

电通量等于电场与dA的分。机翻

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高等数学之美

3.In the example we were looking at, dot products certainly aren't preserved.

在我们看到的示例中,当然不会被保留。机翻

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玩转物理学

4.Rather than using the dot product equation, let's use the electric flux equation  without the dot product.

我们不使用方程,而使用不带点的电通量方程。机翻

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玩转物理学

5.Electric flux equals the dot product of the electric field and the area, so let's  use that.

电通量等于电场与面,所以我们就使用它。机翻

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高等数学之美

6.But the operation as a whole is not just one dot product but many.

整个操作不仅仅一个点,而多个点机翻

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高等数学之美

7.In fact, transformations which do preserve dot products are special enough to have their own name: Orthonormal transformations.

事实上,保留的变换非常特殊,有的名字:正交变换。机翻

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高等数学之美

8.Some of you might like think of this as a kind of  dot product.

你们中的一些人可能喜欢将其视为一种机翻

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Linear algebra

9.In fact, worthwhile side note here transformations which do preserve dot products are special enough to have their own name.

事实上 值得注意的保留的变换很特别 有的名字。

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Linear algebra

10.So that performing the linear transformation is the same as taking a dot product with that vector the cross product.

所以进行线性变换就等于对这个向量做点也就叉乘。

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Linear algebra

11.Learn what you have learned, and imagine that you don't already know that the dot product relates to projection.

学习你学过的知识 想象一下你还不知道和投影的关系。

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Linear algebra

12.So when two vectors are generally pointing in the same direction, their dot product is positive.

所以当两个向量通常指向同一个方向时 它们的正的。

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高等数学之美

13.Notice, this looks like a dot product between two column vectors, [m1, m2], and [v1, v2].

请注意,这看起来像两个列向量 [m1, m2] 和 [v1, v2] 之间的机翻

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Linear algebra

14.And if they point in generally the opposite direction, their dot product is negative.

如果它们通常指向相反的方向 它们的负的。

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Linear algebra

15.Solving a linear system with an orthonormal matrix is actually super easy, because dot products are preserved.

用标准正交矩阵求解线性方程组其实非常简单 因为被保留了。

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Linear algebra

16.The dot product before and after the transformation will look very different.

变换前后的看起来很不一样。

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Linear algebra

17.When their perpendicular meaning, the projection of one onto the other, is the zero vector, their dot product is zero.

当它们垂直的意思 一个向量在另一个向量上的投影 零向量时 它们的零。

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Linear algebra

18.Luckily, this computation has a really nice geometric interpretation to think about the dot product between two vectors V and W.

幸运的 这个计算有一个很好的几何解释来考虑两个向量V和W之间的

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高等数学之美

19.For most linear transformations, the dot product before and after the transformation will be very different.

对于大多数线性变换,变换前后的有很大不同。机翻

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Linear algebra

20.That is, they don't preserve that zero dot product.

也就说 它们不保留0

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