连分数中的矩阵运算

Matrix Operations in Continued Fractions

摘要: 本文旨在探究矩阵运算在连分数中的应用。本文通过欧几里得算法自然地引出连分数的概念，探究了矩阵运算在连分数中的若干应用，利用矩阵运算技巧证明了连分数的部分性质，通过实例展示矩阵在连分数中的巧妙应用。矩阵运算在连分数中有着广泛而深入的应用，为我们深入理解和研究连分数提供了新的视角和工具。

Abstract: This article aims to explore the application of matrix operations in continued fractions. This article naturally introduces the concept of continued fractions through Euclidean algorithm, explores several applications of matrix operations in continued fractions, proves some properties of con-tinued fractions using matrix operation techniques, and demonstrates the ingenious application of matrices in continued fractions through examples. Matrix operations have extensive and in-depth applications in continued fractions, providing us with new perspectives and tools for in-depth un-derstanding and research of continued fractions.