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

by Michael Sormani (College of Staten Island CUNY)

This article originally appeared in:
Mathematics Magazine
April, 2000

Subject classification(s): Algebra and Number Theory | Linear Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

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  Historical references are included.

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Capsule Course Topic(s):
Linear Algebra | Eigenvalues and Eigenvectors
Linear Algebra | History of Linear Algebra
Linear Algebra | Matrix Algebra
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