# Matrices, Continued Fractions, and Some Early History of Iteration Theory

Continued fractions of the form $$\frac{1}{1 + \frac{c}{1 + \frac{c}{ 1 +\ddots}}}$$ are analyzed using linear algebra and iteration theory.  The continued fractions of interest are closely related to a class of $$2 \times 2$$ matrices, and the eigenvalues and eigenvectors of those matrices are investigated to determine when the corresponding continued fractions converge.  Historical references are included.

Old Node ID:
3401
MSC Codes:
97H60
Author(s):
Michael Sormani (College of Staten Island CUNY)
Publication Date:
Monday, February 8, 2010
Original Publication Source:
Mathematics Magazine
Original Publication Date:
April, 2000
Subject(s):
Algebra and Number Theory
Linear Algebra
Topic(s):
Linear Algebra
Eigenvalues and Eigenvectors
History of Linear Algebra
Matrix Algebra
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File Content:
Rating Count:
22.00
Rating Sum:
65.00
Rating Average:
2.95
Applicable Course(s):
3.8 Linear/Matrix Algebra
Modify Date:
Monday, February 8, 2010