Continued Fraction Expansions of Matrix Eigenvectors

Details Continued Fraction Expansions of Matrix Eigenvectors Continued Fraction Expansions of Matrix Eigenvectors

2008-10-11

arxiv.org/abs/0810.2054v1

Mathematics

Number Theory

10 pages, 7 figures

Scientific paper

We examine various properties of the continued fraction expansions of matrix eigenvector slopes of matrices from the SL(2, Z) group. We calculate the average period length, maximum period length, average period sum, maximum period sum and the distributions of 1s 2s and 3s in the periods versus the radius of the Ball within which the matrices are located. We also prove that the periods of continued fraction expansions from the real irrational roots of x2 + px + q = 0 are always palindromes.

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