| Article ID: | iaor20072570 |
| Country: | United States |
| Volume: | 29 |
| Issue: | 4 |
| Start Page Number: | 776 |
| End Page Number: | 785 |
| Publication Date: | Nov 2004 |
| Journal: | Mathematics of Operations Research |
| Authors: | Lewis A.S. |
An important measure of conditioning of a conic linear system is the size of the smallest structured perturbation making the system ill-posed. We show that this measure is unchanged if we restrict to perturbations of low rank. We thereby derive a broad generalization of the classic Eckart–Young result characterizing the distance to ill-posedness for a linear map.