Title: Condition number and matrices,
Abstract: It is well known the concept of the condition number $\kappa(A) =
\|A\|\|A^{-1}\|$, where $A$ is a $n \times n$ real or complex matrix and the
norm used is the spectral norm. Although it is very common to think in
$\kappa(A)$ as "the" condition number of $A$, the truth is that condition
numbers are associated to problems, not just instance of problems. Our goal is
to clarify this difference. We will introduce the general concept of condition
number and apply it to the particular case of real or complex matrices. After
this, we will introduce the classic condition number $\kappa(A)$ of a matrix
and show some known results.