1. Error handling in linear algebra

1.1 Problem position

The problem is essentially this: given a linear operator u, if a vector x is known to an accuracy ε, what accuracy can we expect for the vector u (x)? The notion of precision of a vector will be detailed by introducing norms. We will also study the inverse problem, relating to u ^-1 , which is essentially that of determining the precision of a solution to a linear equation.

Readers may wish to consult the article [A 101] Functional analysis.