Linear algebra has various important applications in mathematics, physics and technology, so it occupies a primary position in all branches of algebra. With the wide application of computers today, computer graphics, computer-aided design, cryptography, virtual reality and other technologies all take linear algebra as a part of their theoretical and algorithmic basis.

The connection between geometric concepts and algebraic methods embodied in linear algebra, axiomatic methods abstracted from concrete concepts, strict logical deduction and ingenious induction and synthesis are very useful for strengthening people's mathematical training and obtaining scientific intelligence.

With the development of science, it is necessary to study not only the relationship between single variables, but also the relationship between multiple variables. In most cases, all kinds of practical problems can be linearized, and with the development of computers, linearized problems can also be calculated. Linear algebra is a powerful tool to solve these problems. The calculation method of linear algebra is also a very important content in computational mathematics.

The meaning of linear algebra is expanding with the development of mathematics. The theory and method of linear algebra has penetrated into many branches of mathematics, and it is also an indispensable basic knowledge of algebra in theoretical physics and theoretical chemistry.

Modern linear algebra with extended data has been extended to study arbitrary or infinite dimensional space. A vector space with dimension n is called an n-dimensional space. Most useful conclusions in 2D and 3D spaces can be extended to these high-dimensional spaces. Although it is difficult for many people to imagine a vector in N-dimensional space, such a vector (that is, an N-tuple) is very effective for representing data.

Because as an n-tuple, vector is an "ordered" list of n elements, most people can effectively summarize and manipulate data under this framework.

For example, eight-dimensional vectors can be used in economics to represent the gross national product (GNP) of eight countries. When arranging the order of all countries, such as (China, America, Britain, France, Germany, Spain, India and Australia), you can use vectors (V 1, V2, V3, V4, V5, V6, V7 and V8) to show their respective GNP in a certain year. Every country's GNP here is in its own position.

References:

Baidu encyclopedia-linear algebra