The Properties Of Transfer Matrices Of General Sierpinski Gasket

Fractal is the morphological characteristics which is filled of non-integer dimen-sions,fractal geometry is the geometry of an irregular geometry of the object.Fractal theorieshave so many important values and applications that we need to explore new fractal struc-tures and properties. We have known some matrix knowledge,and an algebra of matricesof order2^|E|was introduced by Mandelbrot et al,some of the matrices are called transfermatrices of fractals of associated with iterative constructions.Transfer matrices of fractals are special kind of matrices,some of properties are intro-duced in some articles by Mandelbrot et al.It was proved that the eigenvalues of the transfermatrices of fractals are non-negative integers and its eigenvectors have some special orthog-onality relations and are real.In this paper,further properties and the proof of diagonalizationof these matrices are shown,as well as the process of implementation.The first part is the introduction,it mainly reviews the known results and makes someremarks,and then introduces the background and significance of the study.Then,somerelevant definitions and marks are given.In the third part,we give some propositions’proof,especially the matrices calculations, as well as the proof of the theorem about theeigenvalues and eigenvectors,and the transfer matrices of fractals are shown to be diago-nalizable.In the last chapter, we give the promotion and the process of implementation,wecan ask if these transfer matrices of fractals associated with the notion of the invariantchessboard under the action of a group sill possess the properties in part three.We also giveexamples of the process of solving the eigenvalues and eigenvectors of the transfer matricesof general Sierpinski gasket for the order2^|E|and less than2^|E|and their diagonal matrices.