A real matrix has all real entries.
i (j) is called the row (column) subscript.
An m_n matrix is said to be of size (or dimension) m_n.
If m=n the matrix is square of order n.
The ai,iís are the diagonal entries.
Operations on matrices are very useful in real life (go over handout on Digital Images and applications to x-rays and prosecution of Damian Williams).