In the matrix, e generally represents identity matrix, E 1 is a first-order matrix, E2 is a second-order matrix, and E3 is a third-order 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, 3D animation also needs matrices. Matrix operation 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.