A unique hedge can still react strongly to small target changes. The condition number measures worst-case relative sensitivity for a linear solve. This note derives the bound from singular values and explains why determinant magnitude alone is unreliable. We keep the matrix fixed when perturbing the target, so the assumptions of the bound remain explicit.
Learning objectives. By the end of this note you should be able to:
- define the condition number via the SVD and compute it for a small matrix;
- state the perturbation bound the condition number controls;
- explain why , not , is the right diagnostic for near-singularity;
- distinguish a well-conditioned from an ill-conditioned problem in a financial example.
In this lesson
- Definition and the perturbation bound
- Condition number versus determinant
Before you start
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