Let's say that I have a linear system $Ax=b$, where $A$ is square matrix $nxn$, $x$ - searching variable, and $b$ - vector $nx1$.
I solved this equation and got a solution.
Then I changed some of the vectors $b$ values with small variation (added/subtracted a number close to zero). And then also solved that system.
Depending on linear systems matrix $A$ and vector $b$ initial values the $x$ variables might change a lot or have a small different. I tried to figure out on what that depends. Is it somehow related with eigenvalues of matrix $A$?
Any ideas? Thanks in advance.