1. Describe and solve practical problems: Linear algebra provides tools for dealing with concepts such as linear equations, vector space and linear transformation, and is widely used in physics, engineering, computer science and other fields. For example, current and voltage in circuit analysis can be represented by vectors, and matrix operation can be used to solve complex network problems.
2. Learning abstract structure: Linear algebra not only pays attention to specific numerical values, but also pays attention to the structure and relationship behind the data. By learning abstract concepts such as vector space and linear mapping, we can deeply understand the geometric characteristics and algebraic structure of data, which is very important for data mining, machine learning and other fields.
3. Providing theoretical basis: Linear algebra provides theoretical basis for many mathematical fields. For example, derivatives and integrals in calculus can be regarded as the limits and integrals of vectors and matrices in linear algebra; Random variables and probability distribution in probability theory can be regarded as vector space and linear mapping; The linear programming problem in optimization theory can also be attributed to the problem of linear algebra.
4. Develop new mathematical tools and methods: The development of linear algebra promotes the emergence of new mathematical tools and methods. For example, the development of matrix theory has produced important concepts such as matrix decomposition, eigenvalues and eigenvectors, which are widely used in signal processing, image processing and other fields. The development of linear mapping theory has produced important mathematical tools such as Fourier transform and Laplace transform, which play an important role in signal processing, partial differential equations and other fields.
Generally speaking, linear algebra has many functions in mathematics. It not only provides a practical tool to deal with practical problems, but also provides a theoretical basis for understanding and studying complex structures, and also promotes the development of new mathematical tools and methods.