A brief historical introduction to matrices and their applications

Abstract

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer’s Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical networks. It contains a wide variety of important materials accessible to college and even high school students and teachers at all levels.

Keywords:

• magic squares
• matrices
• determinants
• algebra of matrices and special matrices

2010 AMS Mathematics subject classification codes:

• 01-02
• 15-02
• 15A03

Acknowledgements

The author expresses his gratitude to the referees for suggesting improvements in the exposition of the paper.