Matrix notation is a compact way to represent and manipulate data in mathematics and computer science. A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, a matrix with two rows and three columns can be written as A = \beginpmatrix a_11 & a_12 & a_13 \\ a_21 & a_22 & a_23 \endpmatrix. This notation simplifies complex calculations, such as solving systems of equations or performing transformations in linear algebra. In matrix notation, operations like addition, subtraction, and multiplication can be performed efficiently. Each element in a matrix is identified by its position, using indices such as a_{ij}, where i represents the row and j represents the column. This structured approach is widely used in various fields, including statistics, physics, and machine learning, making it easier to handle large