Matrices 

A matrix (pl. matrices) is a group of numbers listed in a rectangular array. The group of numbers is usually either in brackets [ ] or in parenthesis ( ), as in the following:

It’s also customary to name a matrix by a capital letter, so let’s name the one on the left A and the one on the right B.

The size (sometimes called order or dimension) of a matrix is specified by the number of rows and the number of columns it has. For example, the size of matrix A is 2 × 3 (read as 2 by 3) since there are it has two rows and three columns. The size of a matrix is always indicated by the number of rows first, followed by the number of columns, and never the other way around. Therefore, the size of matrix B is 4 × 2, instead of 2 × 4.

Each number in a matrix is called an entry. Since a matrix has more than one entry, each entry is indicated by a position. For example, as a position, the 6 in matrix A is a₂₃, where a is the lower case of A, the matrix, 2 and 3 are the row and column 6 is in, respectively. Therefore, the position of the 6 in matrix B is b₃₂ since 6 is in the 3^rd row and 2^nd column of matrix B.  

Special Matrices

There are special kinds of matrices. For example, if a matrix has the same number of rows and columns, it’s called a square matrix. If a matrix has only one row, it’s called a row vector. If a matrix has only one column, it’s called a column vector.  Vectors are a special kind of matrices that have its own realm of applications, so sometimes we don’t even consider they belong the matrix family.