In mathematics and computer science, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are widely used in various fields such as linear algebra, statistics, physics, engineering, and computer graphics. They play a crucial role in solving systems of linear equations, representing transformations and operations on data, and storing and manipulating information in a structured format. Matrices are usually denoted by uppercase letters, with the number of rows and columns specified in the form "m x n" where "m" is the number of rows and "n" is the number of columns. Operations on matrices include addition, subtraction, scalar multiplication, matrix multiplication, transposition, inversion, and determinant calculation. Research in matrix theory involves studying properties, operations, and applications of matrices, as well as developing algorithms and techniques for solving matrix-related problems efficiently. Some important topics in matrix theory include eigenvalues and eigenvectors, singular value decomposition, matrix factorization, sparse matrices, and applications in machine learning, signal processing, image processing, and network analysis.