Fibonacci数列的性质及矩阵证明

The Property of Fibonacci Sequence and the Proof of Matrix

运用矩阵方法证明了Fibonacci数列的通项公式及Cassini公式,并对Cassini公式进行了推广,进而得到一个结论-由连续的m×r个Fibonacci数的k次方所组成的m行r列矩阵D m×rk,当r,m≥k+1,k=1,2,3时,矩阵的秩都为k+1．

Prove the general term formula of Fibonacci sequence and Cassini formula are proved in terms of Matrix theory, Cassini formula is generalized.If ro,r≥k＋1 and k=1,2,3, the roxr Matrix Dk made up of k-th power of continuous Fibonacci numbers is k＋1.