Cayley And Matrix Theory Foundation

Based on interpretation and research to Cayley’s three matrices papers,this paper is main to do the work in the following areas:Firstly,on the basis of reading the original "A menoir on the theory of matrices",introduced in matrix notation,the matrix’s basic concepts,basic arithmetic and basic properties,given on explanation to establish some important theorems.Pointed out the paper published,making the birth of the matrix theory.Cayley is the founder of the well-deserved matrix theory.Secondly,through interpretation and analysisthe the second article "A supplementary memoir on the theory of matrices" by Cayley,and further found that it is the nature of the matrix complement and expand,while the introduction of the Hermitian matrix and automorphisms transform of the function,obtained that Hermitian matrix is the automorphisms transformation matrix of the function.Thirdly,on the basis of researching Cayley’s third paper"On the Matrical equation qQ-Qq’=0",focusing analysis method for solving the matrix equation.Pointed out:in the form of a matrix representation of quaternions,and proposed the concept of matrix equations.Opened up the way to solve the matrix equation.