In mathematics, a matrix is a group of complex numbers or real numbers arranged in a rectangular array, which originated from a square matrix composed of coefficients and constants of an equation. This concept was first put forward by British mathematician Kelly in19th century.

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.

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. 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.

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1925 In the list of approved nouns published in the fourth issue of Science Volume 10, the matrix is translated into a matrix, the square matrix is translated into a square matrix, and various matrices such as orthogonal matrix and adjoint matrix are translated into a square matrix.

1935, the "matrix" first appeared as a translated name in the "Mathematical Terminology" approved by the Ministry of Education of the Republic of China (and "ordered all colleges and universities in China to follow it to show unity").

1938, Cao Huiqun thinks that the proper translation name in the glossary of arithmetic terms is "long square matrix", which was revised by the Scientific Terminology Review Committee. In Mathematical Nouns compiled by People's Republic of China (PRC) after the founding of the People's Republic of China, it was translated as "(moment) matrix".

From 65438 to 0993, "matrix" was officially translated in "Mathematical Terminology" published by China Natural Science Terminology Examination Committee, which is still in use today.