The first function of linear algebra is to abstract concrete things into mathematical objects. In fact, for linear algebra, we can make a simple definition. What is the so-called linear algebra? It is the combination of quantity and structure, that is, linear algebra equals quantity plus structure. This number itself is an independent number. We don't have a single number structure, and we don't have a single object structure. But when we arrange a group of numbers or a bunch of numbers together, this arrangement is not random, but has a certain order. At this time, the order between numbers or the order between numbers forms a structure, which can contain certain information and can be used by us.
Of course, structure has another meaning. We can define some operations about quantity. In linear space, we mentioned that basic operations include addition, including number multiplication and so on. With operation, we can put different objects together and arrange them in a certain order to form a vector and form such an object. Then through some operations such as addition and multiplication, we can do more operations on this object. Thus, the process of abstracting concrete things into mathematical objects is realized. This is the most important function of linear algebra. Of course, not only in machine learning, but also in other applications of linear algebra: abstracting concrete things into mathematical objects.
The second function of linear algebra is to improve the efficiency of large-scale operation. Another function of linear algebra is to improve the efficiency of large-scale operations. Because in modern machine learning, the data we have to deal with is massive data, and the amount of data is growing exponentially. We have to deal with more and more data. If we simply use the most traditional method and use a for loop to deal with high-dimensional matrices, its efficiency is definitely quite low. With linear algebra, we can introduce the operation of matrix into the algorithm of machine learning, and improve the efficiency of large-scale operation through some extra libraries or some extra software packages.
In this article, we introduced you to the related knowledge of linear algebra. Through the understanding and learning of linear algebra, we can better understand and master machine learning. In this article, I believe everyone has understood the function of linear algebra, and I hope this article can help you better.