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Special Interest **Up:** Continued Fraction Factorization **Previous:**
Motivation and Examples

As Justin Miller describes in his report Families
of Continued Fractions, there is a fundamental corresponce
between continued fractions and matrices. This is a consequence
of the fact that if , then

where is
the ith convergent of the continued fraction expansion of . This
correspondence will be the basis for the method of factorization
described in this report. Let represent the matrix product

Since we are interested in the string in the expansion , it will be convinient to
use the following declaration throughout this report:

The final tool we will use in this report
involves a type of function known as a fractional linear
transformation. For a matrix and a real number , the fractional
linear transformation is defined as follows:

We are now ready to introduce and prove certain theorems that are of special interest in regards to this report.

**Next:** Theorems of
Special Interest **Up:** Continued Fraction Factorization **Previous:**
Motivation and Examples