The items contained in a matrix are its entries; an entry is a single piece of data from within a matrix. Matrix notation refers to the use of a subscript to identify the row and column location of a single entry within a matrix.
A matrix is written in brackets, which contain rows and columns of data, and has dimension, which is the number of rows and columns contained within the matrix. By mathematical convention, the dimension of a matrix is written as rows by columns.
Matrices with the same dimension are added and subtracted by performing the indicated operation on each matrix entry with the corresponding notation. Matrices that are not the same dimension cannot be added or subtracted.
There are two types of matrix multiplication, scalar and matrix. Scalar refers to the multiplication of each entry of a matrix by a single number or variable. Matrix refers to the multiplication of one matrix by another and is only possible when one matrix contains a number of rows equal to the number of columns in the other matrix. The resulting matrix has the dimension of non-corresponding rows and columns. For example, a 12 by 15 matrix multiplied by a 15 by 13 matrix results in a 12 by 13 matrix. Matrices that do not contain a corresponding number of rows to columns cannot be multiplied.