In numerical linear algebra, we create ways for a computer to solve a linear system of equations . In doing so, we analyze how efficiently and accurately we can find the solution .
Perturbation theory concerns how much error we incur in the solution when we perturb (spoil) the data and . A classic statement tells us that the amount of error depends on the condition number of the matrix .
I will define and prove the statement, and help you understand it by “hearing” it.