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 AlgebraApplicable Course(s):
3.8 Linear/Matrix AlgebraContinued 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 Historical references are included.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