In mathematics, matrices are simply an organized table of numbers. The reason they are used is because scientists and mathematicians have found that some numerical problems (generally systems of equations) can be solved algorithmically when the data placed into the problem is organized this way. In mathematics, a row or column of a matrix is termed a "vector", though R has a vector data structure that is not the same thing as the row or column of a matrix. The numbers characterizing a vector in mathematics are thought of as the endpoint of that vector with vector's origin at the origin of the coordinate system (this is what we term a "vector" mathematically, but it is really a point).

While the term "matrix" is often used to refer to a rectangular arrangement for string data (that is, a table), we must be much more cautious with our use of the term in numeric computation since R has more than one way to store composite variables.