Mine were humanities and linear algebra.

我学的是人文学科和线性代数。

The Metal Performance Shaders Library provides an optimized set of image processing, linear algebra, and other compute operations.

Metal 性能着色程序库提供了一整套优化的图像处理、线性代数以及其他计算操作方法。

He needs to get from his linear algebra class to his physics class, which is 822 meters away.

他需要从线性代数课堂教室赶到距离822米的物理学教室。

This pattern shows up a lot in linear algebra.

这种模式在线性代数中经常出现。

Similar rules are used in linear algebra and computer graphics to make sure shapes don't get distorted as we're tormenting them with rotations, translations and more.

类似的规则用于线性代数和计算机图形，以确保当我们对它们进行旋转、转换和其它更多操作时，图形不会被扭曲。

They are more like hundred step functions that use differentiable linear algebra to approximate correlation between adjacent brain states.

它们更像是百步函数，使用可微线性代数来近似相邻大脑状态之间的相关性。

Arguably, it falls outside the essence of linear algebra.

可以说 它超出了线性代数的本质。

Take a moment to imagine yourself right now, as a mathematician developing the theory of linear algebra.

花点时间想象一下你自己 作为一个数学家正在发展线性代数理论。

1st A few words on the usefulness of linear algebra.

首先简单介绍一下线性代数的有用性。

Vectors, core topics in linear algebra, like determinants and eigenvectors, seem indifferent to your choice of coordinate systems.

向量 线性代数的核心主题 像行列式和特征向量 似乎与你选择的坐标系无关。

After all, every topic in linear algebra is going to center around these two operations.

毕竟 线性代数的每个主题都会围绕着这两个运算展开。

Remember how I said that linear algebra revolves around vector edition and scalar multiplication?

还记得我说过线性代数围绕着向量编辑和标量乘法吗？

And doing that usually relies on a lot of linear algebra understanding.

这通常依赖于对线性代数的理解。

In fact, throughout linear algebra, one of the main things that numbers do is scale vectors.

事实上 在线性代数中 数字最主要的作用之一就是缩放向量。

In linear algebra, it's almost always the case that your vector will be rooted at the origin.

在线性代数中 向量总是在原点处有根。

But luckily, linear algebra limits itself to a special type of transformation, ones that are easier to understand, called linear transformations.

但幸运的是 线性代数将自己局限于一种特殊的变换 一种更容易理解的变换 叫做线性变换。

Now, the more linear, algebra oriented way to describe coordinates is to think of each of these numbers as a scaler, a thing that stretches or squishes vectors.

现在 更线性的 代数化的描述坐标的方法是把每一个数字看作一个标量 一个拉伸或压缩向量的东西。

Wrapping your mind around this concept is going to help consolidate ideas from linear algebra, like the determinant and linear systems, by seeing how they relate to each other.

把你的思维围绕在这个概念上有助于巩固线性代数的概念 比如行列式和线性系统 通过观察它们之间的关系。

I've been greatly inspired and heckled to do this by my friend Grant Sanderson of Three Blue One Brown who set the standard for this kind of thing with his excellent series on calculus and linear algebra.

我受到了我朋友Grant Sanderson极大的启发，他在微积分和线性代数方面的一系列视频都很棒，并为这类视频设定了一个标准。

This definition of addition, by the way, is pretty much the only time in linear algebra where we let vectors stray away from the origin.

顺便说一下 这个加法的定义 几乎是线性代数中唯一一次让向量偏离原点。