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.

Matrix decomposition:

A matrix is decomposed into the sum or product of several relatively simple or characteristic matrices. Matrix decomposition methods generally include triangle decomposition, spectral decomposition, singular value decomposition, full rank decomposition and so on.

In linear algebra, similar matrix refers to a matrix with similar relationship. Similarity relation is the equivalent relation between two matrices. The two n×n matrices A and B are similar matrices if and only if there is an n×n invertible matrix P..