This section is proposed to be a catch all for several of the fundamental concepts which are used occasionally in working with systems of differential equations. There will not be many details under this section, nor will we be working large numbers of illustrations. Also, in various cases we will not be looking at the common case as we won't require the general cases in our differential equations work.

Let's begin with some of the basic notation for matrices. An n x m matrix (it is often termed as the size or dimension of the matrix) is a matrix along with n rows and m columns and the entry in the ith row and jth column is denoted through a_ij. A short hand method of writing a common n x m matrix is the subsequently,

= (a_ij)_m×n

The dimension or size of a matrix is subscripted as demonstrated if needed. If it's not needed or clear from the problem the subscripted size is often dropped by the matrix