A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics and computer science to represent data, solve systems of equations, and perform various calculations. Each element in a matrix is identified by its position, typically denoted as a_ij, where i represents the row and j represents the column. Matrices can be added, subtracted, and multiplied, following specific rules. They are also essential in fields like physics, engineering, and statistics, where they help model complex systems and analyze relationships between variables.