The N -th Power Of A 2×2 Matrix And Its Application

Using 2×2 Matrix to study the combinatorial identities, Aim is to find and certify combinatorial identities, the main contents of this paper is as follows:The paper Introduced combinatorial identities and their research methods,the application of the n-th power of a 2×2 matrix and its research also this thesis used the concepts, the fundamental theorems and conclusions.In this paper I introduce n-th power of a 2×2 matrix and its application of searching and proving the combinatorial identities.More precisely, I generalize the following:Let (?) be an arbitrary 2×2 matrix, T=a+d its trace, D=ad-bc its determinant and define Then, for n≥1,I use the n-th power of particular 2×2 matrices, the exchange quality of the matrix,and Fibonacci sequences and Lucas sequences to derive twelve combinatorial identities.In addition, according to n-th power of a 2x2 matrix and its application of searching and proving the combinatorial identities, I use the n-th power of particular n x n matrices to derive a combinatorial identity.