Matrix

A

**matrix** is a rectangular table of

*elements* (usually called

*entries*), which may be

numbers.. We are only going to work with matrices which entries are real numbers.

The horizontal lines in a matrix are called

**rows** and the vertical lines are called

**columns**. A matrix with

*m* rows and

*n* columns is called an

*m*-by-

*n* matrix (written

*m* ×

*n*) and

*m* and

*n* are called its

**dimensions**.

(Frecuently an

*m*-by-

*n* matrix is said to has an

**order** of

*m* ×

*n* ("order" = "size")).

A 3x3 matrix can be:

While a general mxn matrix is:

that can be written as:

A = (a_{ij} ), where i=1,...,n and j=1,2,...,m
Observe that almost always upper-case letters denote matrices, while the corresponding lower-case letters, with two subscript indices, represent the entries, for example, the *(i,j)*^{th} entry of a matrix **A** is most commonly written as *a*_{i,j}.