We're almost at the point where we have a high-quality unified vector space.

EM：我们几乎已经到了拥有高质量统一向量空间的地步。

The next and final video of this series is going to be on abstract vector spaces.

本系列的下一个视频 也是最后一个视频 将讨论抽象向量空间。

These sets of vectorish things, like arrows or lists of numbers or functions, are called vector spaces.

这些向量的集合 如箭头 数字列表或函数 被称为向量空间。

And you, as the mathematician, never have to think about all the possible crazy vector spaces people might define.

作为数学家 你永远不需要考虑人们可能定义的所有疯狂的向量空间。

Sin goes with vectors, which have many embodiments, but math abstracts them all into a single, intangible notion of a vector space.

Sin与向量一起 它有很多体现 但数学将它们都抽象为一个单一的 无形的向量空间概念。

And what you, as the mathematician, might want to do is say, hey, everyone, I don't want to have to think about all the different types of crazy vector spaces that you might come up with.

作为数学家 你们可能会说 嘿 各位 我不想考虑你们可能想到的所有不同类型的疯狂向量空间。

These rules are called axioms. And in the modern theory of linear algebra, there are eight axioms that any vector space must satisfy If all of the theory and constructs that we've discovered are going to apply.

这些规则被称为公理 在现代线性代数理论中 有八个公理是任何向量空间都必须满足的如果我们发现的所有理论和构造都适用的话。

These axioms are not so much fundamental rules of nature as they are an interface between you, the mathematician discovering results, and other people who might want to apply those results to new sorts of vector spaces.

这些公理与其说是自然的基本规则 不如说是你 发现结果的数学家 和其他可能想把这些结果应用到新类型的向量空间的人之间的接口。