Do you know if he'll be doing the full color octet calculations?

你知道他会不会教用矩阵乘法做八色胶子运算吗？

The most important kind of magical step is laying them out in a matrix and doing what's called matrix multiplication.

最关键的神奇步骤是将它们排列成矩阵，并进行所谓的矩阵乘法。

Applying One transformation after another is captured algebraically with matrix multiplication.

应用一个接一个的变换是用矩阵乘法代数捕获的。

You might notice that this looks a lot like matrix vector multiplication.

你可能注意到这看起来很像矩阵向量乘法。

Easier to think about rotations performing This matrix multiplication numerically is, once again, pretty similar to the two dimensional case.

考虑旋转执行这个矩阵乘法的数值运算 再一次 和二情况很相似。

Once you know that it's linear, you know that there's some way to describe this function as matrix multiplication.

一旦你知道它是线性的 你就知道有一些方法可以用矩阵乘法来描述这个函数。

But when you think about matrix multiplication as applying one transformation after another, this property is just trivial.

但是当你把矩阵乘法看作是应用一个又一个变换时 这个性质就很简单了。

Trust me, this will give you a much better conceptual framework that makes the properties of matrix multiplication much easier to understand.

相信我 这将给你一个好的概念框架 使矩阵乘法的性质理解。

When you do this calculation purely numerically, its matrix vector multiplication.

当你用纯数值的方法计算时 它是矩阵向量的乘法。

In particular, I want to show you a way to think about matrix factor multiplication that doesn't rely on memorization.

特别地 我想向你们展示一种不依赖于记忆的矩阵因子乘法的方法。

No matrix multiplication necessary. I remember when I 1st took linear algebra, there was this one homework problem that asks us to prove that matrix multiplication is associated.

不需要矩阵乘法 我记得我第一次学线性代数的时候 有一道作业要求我们证明矩阵乘法是相关的。

For this next part, it's important that you're all comfortable representing transformations with matrices, and that you know how matrix multiplication corresponds to composing success of transformations.

在接下来的部分中 重要的是你们都能自如地用矩阵表示变换 并且知道矩阵乘法是如何与成功组合变换相对应的。

So, if you wanna build any AI application, you have to have an accelerator, just like we have in the cloud, to be able to run these matrix math multiplications fast in order to drive AI features.

如果你想构建任何人工智能应用的话，你必须拥有一个像云端那样的加速器，以便能够快速运行这些矩阵数学乘法，从而驱动人工智能功能。

For this video, I'm just going to focus on what these transformations look like in the case of two dimensions, and how they relate to the idea of matrix factor multiplication.

在这个视频中 我将关注这些变换在二情况下是什么样子的 以及它们是如何与矩阵因子乘法的思想联系起来的。

So surprisingly, matrix vector multiplication and taking a derivative, which at 1st seem like completely different animals, are both just really members of the same family.

所以令人惊讶的是 矩阵向量乘法和求导 乍一看完全不同的东西 实际上都是同一个家族的成员。

But I really do think that before memorizing that process, you should get in the habit of thinking about what matrix multiplication really represents, applying one transformation after another.

但我真的认为在记住这个过程之前 你应该养成思考矩阵乘法真正代表什么的习惯 应用一个又一个变换。

It's a little awkward to work with at 1st, because that left hand side represents matrix factor multiplication, but the right hand side here is scalar vector multiplication.

首先处理这个有点尴尬 因为左边表示矩阵因子的乘法 但右边是标量向量的乘法。

You could even define this as matrix vector multiplication when you put the matrix on the left of the vector, like its a function.

你甚至可以把它定义为矩阵向量乘法当你把矩阵放在向量的左边 就像它是一个函数。

This is an honest goodness proof that matrix multiplication is associated, and even better than that, it's a good explanation for why that property should be true.

这是一个很好的证明矩阵乘法是相关的 甚至比这好 它很好地解释了为什么这个性质是正确的。

So let's start by rewriting that right hand side as some kind of matrix vector multiplication, using a matrix which has the effect of scaling any vector by a factor of lambda.

我们先把右边写成某种矩阵向量的乘法 用一个矩阵它的作用是将任意向量乘以的倍数。