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Matrix inversion is not robust in the sense that a small difference in the input can give a large difference in the output. Is there an appropriate word to describe such a system?

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Condition number. –  DumpsterDoofus Mar 3 at 14:10
    
By analogy to "robust", "fragile" sounds good –  User58220 Mar 4 at 0:40
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@DumpsterDoofus I know of that related concept, but it is quite specific and also isn't even an adjective. –  Anna Mar 4 at 7:05

2 Answers 2

  • Sensitivity, or
  • sensitive dependence on the input.

Moreover, if your "system" consists of a repeated operation, e.g. $$x_n\to x_{n+1}=f(x_n)$$ the sensitive dependence of $x_n$ on the initial condition $x_0$ is denoted Chaos.

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Related to DumpsterDoofus's comment, I've always seen the adjective "ill-conditioned", which happens to be used on the wikipedia page for condition number

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