On the Distribution of a Scaled Condition Number
- 1 January 1992
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 58 (197) , 185-190
- https://doi.org/10.2307/2153027
Abstract
In this note, we give the exact distribution of a scaled condition number used by Demmel to model the probability that matrix inversion is difficult. Specifically, consider a random matrix A and the scaled condition number <!-- MATH ${\kappa _D}(A) = {\left\| A \right\|_F} \bullet \left\| {{A^{ - 1}}} \right\|$ --> . Demmel provided bounds for the condition number distribution when A has real or complex normally distributed elements. Here, we give the exact formula.
Keywords
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