Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a list of a list of numbers, where each list in the list has the same number of numbers. It's often represented as rectangle of numbers, arranged in rows and columns. The rows are each left-to-right (horizontal) lines, and the columns go top-to-bottom (vertical). The top-left cell is at row 1, column 1 (see diagram at right).

Matrices are often represented by capital roman letters such as ${\displaystyle A}$, ${\displaystyle B}$ and ${\displaystyle C}$,^[1] and there are rules for adding, subtracting and "multiplying" matrices together, but the rules are different than for numbers.^[2] As an example, the product ${\displaystyle AB}$ does not always give the same result as ${\displaystyle BA}$, which is the case for the multiplication of ordinary numbers.^[3] A matrix can have more than 2 dimensions, such as a 3D matrix. Also, a matrix can be one-dimensional, as a single row or a single column.

Many natural sciences use matrices quite a lot. In many universities, courses about matrices (usually called linear algebra) are taught very early, sometimes even in the first year of studies. Matrices are also very common in computer science, engineering, physics, economics, and statistics.^[4]

1. ↑ "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-19.
2. ↑ "Matrices". www.mathsisfun.com. Retrieved 2020-08-19.
3. ↑ "How to Multiply Matrices". www.mathsisfun.com. Retrieved 2020-08-19.
4. ↑ "Matrix | mathematics". Encyclopedia Britannica. Retrieved 2020-08-19.