Published Paper Details:

The matrix is a very useful and significant mathematical construct of contemporary society. Originally formed as a methodical way of solving linear systems of equations, matrix theory has developed into a large framework that supports many disciplines, including quantum physics, linear algebra, numerical analysis, engineering design and most recently, data science. Matrix analysis allows for the development of complex multivariable systems, through the use of a structured, compact representation of linear transformations. Matrices are important in the practical sciences as well as in theoretical mathematics. They are used to create large-scale simulations, optimization methods, and computational models. Computers also rely heavily on matrices for their ability to represent input-output and optimization models in economics, to represent quantum states and coordinate transformations in physics, and in developing machine learning techniques and computer graphic transformations. Through the combination of analytic methods and existing literature, this paper investigates the theoretical foundation, key computational methods and interdisciplinary applications of matrices. The paper illustrates that matrices will remain vital for the development of modern scientific and technological inquiry and will serve as a common mathematical language between various disciplines.