The concept of matrix was gradually formed in19th century. 1800s, Gauss and William Jordan established Gauss-Jordan elimination method. 1844, German mathematician F. Ferdinand F. Eisenstein discussed "transformation" (matrix) and its product. 1850, the British mathematician james joseph sylvester first used the word matrix [2].

British mathematician Arthur Kelly is recognized as the founder of matrix theory. When he began to study matrix as an independent mathematical object, many properties related to matrix were found in the study of determinant, which also made Kelly think that the introduction of matrix was very natural. He said: "I certainly didn't get the concept of matrix through quaternion;" It is either directly derived from the concept of determinant or as a convenient way to express linear equations. "Starting from 1858, he published a series of monographs on matrices, such as Research Report on Matrix Theory, and studied the algorithm, inversion, transposition and characteristic polynomial equation of matrices. Kelly also put forward Kelly-Hamilton theorem, and verified the case of 3×3 matrix, and said that there is no need for further proof. Hamilton proved the case of 4×4 matrix, and the general proof was given by German mathematician F.G.Frohenius in 1898.