Al though not important for my course, I was curious as to why the condition number of a singular matrix is $\infty$. Which also begs the question of what the condition number of a non-invertible non-square matrix would be.
2026-03-25 23:56:31.1774482991
Why is $\kappa(A) = \infty$ if $A$ is a singular matrix?
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The condition number is defined as the ratio between the highest and smallest singular value of the matrix.
If the matrix is singular, then the smallest singular value is $0$.
Thus, the condition numbers tends to $\infty$.