In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. Matrices are used to represent linear maps and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics. Matrices also have important applications in computer graphics, where they have been used to represent rotations and other transformations of images.
Some key concepts associated with matrices include:
- Elements: The numbers that make up the matrix.
- Dimension: The result of the number of rows times the number of columns.
- Order: The number of rows and columns in a matrix.
- Square matrix: A matrix with the same number of rows and columns.
- Invertible matrix: A square matrix that has an inverse.
- Determinant: A scalar value that can be computed from a square matrix.
Matrices can be added, multiplied, and decomposed, so they are commonly used in linear algebra.
