A square matrix is a kind of matrix, especially when the number of rows is equal to the number of columns, the matrix is called a square matrix. Matrix is a common tool in applied mathematics such as advanced algebra and statistical analysis. In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. ?

The operation of extended data matrix is an important problem in the field of numerical analysis. Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application. For some widely used and special matrices, such as sparse matrix and quasi-diagonal matrix, there are concrete fast operation algorithms. For the development and application of matrix related theory, please refer to matrix theory. Infinite-dimensional matrices will also appear in astrophysics, quantum mechanics and other fields, which is the generalization of matrices.

The main branch of numerical analysis is devoted to the development of effective algorithms for matrix calculation, which has been a topic for a century and is an expanding research field. The matrix decomposition method simplifies the theoretical and practical calculation. The customized algorithm for specific matrix structures (such as sparse matrix and near-angle matrix) speeds up the operation speed in finite element method and other calculations. Infinite matrix appears in planetary theory and atomic theory. A simple example of infinite matrix is the matrix representing the derivative operator of Taylor series of functions.