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

我们不使用点积方程，而是使用不带点积的电通量方程。

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

电通量等于电场与dA的点积的积分。

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

但是，让我们使用 E dA 余弦西塔来代替点积。

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积的点积，所以我们就使用它。

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 因为点积被保留了。

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

也就是说 它们不保留0点积。

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

变换前后的点积看起来很不一样。

And looking at the example I just showed, dot products certainly aren't preserved.

看看我刚才举的例子 点积肯定不会被保留。

The relevant background here is understanding determinance, little bit of dot products, and of course, linear systems of equations.

相关的背景知识是理解行列式 一点点积 当然还有线性方程组。

In the sense that applying the transformation is the same thing as taking a dot product with that vector.

在这个意义上应用这个变换就相当于对这个向量做点积。