A matrix serves to perform a linear transformation:
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. Matrices represent linear maps, and allow explicit computations in linear algebra.
A matrix is a rectangular array of numbers; a collection of related entries. The numbers, symbols, or expressions in the matrix are called its elements. The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively. An n-by-n matrix is known as a square matrix of order n.
The determinant of a square matrix A (denoted by det(A) or |A|) is a number encoding certain properties of the matrix. Its absolute value equals the area of the image of the unit square.
Multiplication of two matrices is only vallid if the number of columns of the first matrix is the same as the number of rows of the second matrix. Matrix multiplication is not commutative.
Division is accomplished through a multiplication of the inverse: A/B = A.(B-1)
