  We assume that every element of a matrix has a small, individual error, and
model it by an external number, which is the sum of a nonstandard real number
and a neutrix, the latter being a convex (external) set having the group
property. The algebra of external numbers formalizes common error analysis,
with rules for calculation which are a sort of mellowed form of the axioms for
real numbers.
  We extend the algebra of external numbers to matrix calculus. Many classical
properties continue to hold, sometimes stated in terms of inclusion instead of
equality. There are notable exceptions, for which we give counterexamples and
investigate suitable adaptations. In particular we study addition and
multiplication of matrices, determinants, near inverses, and generalized
notions of linear independence and rank.
