linear algebra is a branch of mathematics whose research objects are vectors, vector spaces (or linear spaces), linear transformations and finite-dimensional linear equations. vector space is an important topic in modern mathematics; linear algebra is widely used in abstract algebra and functional analysis; linear algebra can be concretely expressed through analytic geometry. the theory of linear algebra has been generalized into operator theory. since nonlinear models in scientific research can usually be approximated as linear models, linear algebra is widely used in natural sciences, engineering, computer science and social sciences.

in mathematics, a matrix refers to a two-dimensional data table arranged vertically and horizontally. it originally came from a square matrix composed of coefficients and constants of a system of equations. this concept was first proposed by the british mathematician kelly in the 19th century.

matrices are a common tool in advanced algebra and are also commonly used in applied mathematics disciplines such as statistical analysis. in physics, matrices are used in circuits, mechanics, optics and quantum physics; in computer science, matrices are also used in three-dimensional animation production. matrix operations are an important issue in the field of numerical analysis. decomposing a matrix into combinations of simple matrices can simplify matrix operations both theoretically and practically. there are specific fast operation algorithms for some widely used matrices with special forms, such as sparse matrices and quasi-diagonal matrices. for the development and application of matrix correlation theory, please refer to matrix theory. in the fields of astrophysics, quantum mechanics and other fields, infinite-dimensional matrices will also appear, which is a generalization of matrices.