斐波那契行列式序列若干问题探究

Research on Several Problems of Fibonacci Determinant Sequence

在斐波那契数列的基础上给出了斐波那契行列式序列,即由行列式序列计算得到的数构成的 一个斐波那契数列,并揭示了二者之间的关系,同时介绍了与斐波那契行列式序列相关的三对角行列式、 海森堡行列式。另外,基于行列式计算方面对三者之间的关系进行了探究,通过实例,将一些行列式化为 三对角行列式、海森堡行列式,借助斐波那契行列式序列,给出了几类特殊行列式值计算的新方法,拓宽了 斐波那契行列式序列的应用。

Based on the Fibonacci sequence, this paper gives a Fibonacci determinant sequence, which is a Fibonacci sequence consisted of the numbers calculated by the determinant, and reveals the relationship between them. At the same time, tridiagonal determinant and Heisenberg determinant related to Fibonacci determinant sequence are also introduced, to construct Fibonacci determinant sequence with tridiagonal determinant and Heisenberg determinant. In addition, based on the determinant calculation, the relationship between the three determinants is explored, that is, some determinants can be transformed into tridiagonal determinants and Heisenberg determinants. And then using the Fibonacci determinant sequence, these determinants can be solved. Several new methods for calculating the value of special determinants are given, which widens the application of Fibonacci determinant sequence.