Some Researches On Lucas Sequences

In the thesis, some existing usual identities of Lucas number are extends to the researches on generalized related identities of Lucas number, and methods for evaluating of usual k-power rank of matrix of Fibonacci sequence are spread to generalized rank of matrix of Lucas sequence, so as to further solve methods for evaluating of some kinds of matrix volume of Lucas sequence.The thesis is divided into 4 chapters.In the first chapter, the thesis mainly introduces the history background and research status of Fibonacci sequence and Lucas sequence, briefly summarizes research background of matrix volume, and points out the innovative points of the thesis at the same time.In the second chapter, using the definition of generalized Lucas sequence {Lnk}k=1∞, square relation, reciprocal relation, determinant and sum relation of continuous several generalized Lucas numbers are studied, thus concrete formulas are deduced.In the third chapter, by means of related knowledge of matrix and determinant, continuous k-power(k=2) matrixes of Lucas sequence and generalized rank of matrix of Lucas sequence are researched, then to derive out testification thinking of related identities.In the fourth chapter, based on current concept of matrix volume and comprehension to related knowledge, the thesis makes a further investigation to matrix volume of Lucas sequence and character problem of generalized matrix volume of Lucas sequence.