The Mathematical Principle of the Linear Cloning System

To solve the problem of the space electric field measurement around the optical electric field sensor,this paper proposed the concept of the clone sensing,built the system of the linear clone and established the system of the corresponding theories.By using the method of the cloning transformation,the vector form of the clones was obtained,which constituted the collection of the clone vectors consistent in character and orthogonal in orientation.The property of clone vectors had been analyzed and the orthogonal cloning transformation theorem conserving the value of clone vectors had been proved.The cloning equation set was built on the basis of scalar product operation and the cloning system was composed by multiple clones;the theorem of non-singular conditions of clone matrix,the mathematical support for the reliable application of the linear cloning system,had been proved in this paper.