如何用在算法线性代数？ [英] How is linear algebra used in algorithms?

问题描述

我的几个同行中已提到，线性代数学习算法时是非常重要的。我已经研究了各种算法和采取了一些线性代数课程，我没有看到连接。因此，如何用在算法线性代数？

Several of my peers have mentioned that "linear algebra" is very important when studying algorithms. I've studied a variety of algorithms and taken a few linear algebra courses and I don't see the connection. So how is linear algebra used in algorithms?

例如什么有趣的东西可以一用一连接矩阵图形？

For example what interesting things can one with a connectivity matrix for a graph?

推荐答案

三个具体的例子：

• 线性代数是现代3D图形贯之。这基本上是你在学校学到的同样的事情。该数据被保存在被投影在二维表面上，这是你在屏幕上看到一个三维空间。
• 大多数搜索引擎基于线性代数。这样做是为了重新present每个文档作为载体在一个超空间并查看矢量涉及彼此在该空间中。这是所使用的 Lucene项目，在其他之中。请参见 VSM 。
• 一些现代的COM pression算法，例如所使用的的Ogg Vorbis格式的一种是基于线性代数，或者更具体地被称为矢量量化。

• Linear algebra is the fundament of modern 3d graphics. This is essentially the same thing that you've learned in school. The data is kept in a 3d space that is projected in a 2d surface, which is what you see on your screen.
• Most search engines are based on linear algebra. The idea is to represent each document as a vector in a hyper space and see how the vector relates to each other in this space. This is used by the lucene project, amongst others. See VSM.
• Some modern compression algorithms such as the one used by the ogg vorbis format is based on linear algebra, or more specifically a method called Vector Quantization.

基本上它归结为一个事实，即线性代数是一个非常强大的方法，当有多个变量处理，并有设计算法时以此为理论基础带来巨大的利益。在许多情况下，这种基础并不像你想象的那样appearent，但这并不意味着它不存在。这很可能是你已经实现算法，这将是非常困难的，而不linalg派生。

Basically it comes down to the fact that linear algebra is a very powerful method when dealing with multiple variables, and there's enormous benefits for using this as a theoretical foundation when designing algorithms. In many cases this foundation isn't as appearent as you might think, but that doesn't mean that it isn't there. It's quite possible that you've already implemented algorithms which would have been incredibly hard to derive without linalg.

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