Matrix theory is a branch of mathematics that focuses on the study of matrices, which are rectangular arrays of numbers or symbols arranged in rows and columns. It provides tools for solving systems of linear equations, performing transformations in geometry, and analyzing data in various fields such as computer science and engineering. In matrix theory, operations like addition, multiplication, and finding determinants are fundamental. Matrices can represent graphs, linear transformations, and even complex systems in physics. Applications of matrix theory extend to areas like machine learning, quantum mechanics, and economics, making it a vital component of modern mathematics.