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

你道他会不会教用矩阵乘法做八色胶子运吗？

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。

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捕获的。

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

更容易考虑旋转执行这个矩阵乘法的值运 再一次 和二维情况很相似。

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

一旦你道它是线性的 你就道有一些方法可以用矩阵乘法来描述这个函。

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

当你用纯值的方法时 它是矩阵向量的乘法。

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 这将给你一个更好的概念框架 使矩阵乘法的性质更容易理解。

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。

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 并且道矩阵乘法是如何与成功组合变换相对应的。

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 甚至比这更好 它很好地解释了为什么这个性质是正确的。

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表什么的习惯 应用一个又一个变换。

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。

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。

One of the most important consequences of these properties, which makes matrix factor multiplication possible, is that a linear transformation is completely described by where it takes the basis vectors.

这些性质的最重要的结果之一 使得矩阵因子乘法成为可能 就是线性变换完全由它取基向量的位置来描述。

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。

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维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。

The convention is to record the coordinates of where I had in j hat land as the columns of a matrix, and to define this, some of the scaled versions of those columns by x and y to be matrix vector multiplication.

惯例是记录我在jhat土地上的坐标作为矩阵的列 为了定义这个 这些列被x和y缩放的一些版本是矩阵向量的乘法。