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I'm currently learning about relative condition number (K), and how they are considered as well conditioned or ill conditioned.

From my understanding, a large K value represents ill-conditioned, while a small K value represents well-conditioned.

However, is there a range where K can be labeled as large(ill) or small(well)?

For example, $x^3$ would give a value of $K = 3$ and $x^{1/3}$ would give a value of $K = \frac{1}{3}$. But it doesn't give me the idea if K is large or small, hence I am unable to tell if they are well-conditioned or ill-conditioned.

My apologies for the poor formatting as I am still quite new here.

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Kevin
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Well the post is 4 years old but I think it deserves an answer. Probably the author has found the solution.

If we mean this condition number where $k(A)=\|A\|\|A^{-1}\|$ and $A$ is a matrix, then a large k value means that the matrix is ill-conditioned. This means that if a small change is made in its elements (as it happens when we put data in the computer to make calculations) the solution of the system might differ a lot from the real solution. Thus it can be proved that $k(A)\geq 1$ so I am not sure if the number in the question is the one I am reffering to. As I was tought, a condition number of order larger than $10^5$ is bad (and the matrix is ill-conditioned). A condition number of order (approximately) $1-10^2$ is good (so the matrix is well-conditioned). The range $10^3-10^4$ is something between the two cases (well and ill).

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