Application of matrices

A matrix is a rectangular table of elements (or entries) which may be numbers or more generally any abstract quantities that can be added and multiplied. Matrices find many applications. They are a key tool in linear algebra. One use of matrices in linear algebra is to represent linear transformations. Matrices can also keep track of the coefficients in a system of linear equations. Physics makes use of matrices in various domains, for example, in geometrical optics, mechanics. Graph theory uses matrices to measure distances. Computer graphics uses them to project a 3-dimensional space onto a 2-dimensional screen.

To apply a matrix correctly one should bear in mind its properties. Matrices of the same size can be added and subtracted. Matrices of compatible sizes can be multiplied. These operations have many properties of ordinary arithmetic, except that a matrix multiplication is not commutative, that is, AB and BA are not equal in general.

Matrices have the following properties:

• to add matrices, add corresponding elements together to obtain another matrix of the same order.
• only matrices of the same order may be added.
• to subtract matrices, subtract corresponding elements to obtain another matrix of the same order.
• only matrices of the same order may be subtracted.
• to multiply a matrix by a number (also called a scalar), multiply each element of it.
• to multiply matrices, multiply rows by columns and add.