Timeline for Is there a closed form expression for the inverse of the matrix with elements $A_{i,j}=x_i$ for $i=j$ and $A_{i,j}=1$ for $i\neq j$?
Current License: CC BY-SA 3.0
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| Jun 18, 2011 at 20:40 | comment | added | user15871 | Yes, I noticed that. Interestingly, I used round-about method to reach the solution yesterday, but that was not elegant and it was bothering me (solved for n=2, 3 and extrapolated from there by induction). But your approach is simple and elegant, and right use of Sherman-Morrison formula. Glad I posted the problem on this site. | |
| Jun 18, 2011 at 20:34 | comment | added | Ian Martin | You might also want to rearrange the formulas I give to make it clearer that they work fine if one of the $x_{i}$ equals one. (Obviously the matrix is not invertible if two or more of the $x_{i}$ equal one.) | |
| Jun 18, 2011 at 20:33 | comment | added | user15871 | Thanks Douglas for the reference. As I was working on the problem from your hint, Ian has already posted the solution! Thanks Ian. That's exactly I was looking for. Appreciate your help. | |
| Jun 18, 2011 at 20:30 | vote | accept | user15871 | ||
| Jun 18, 2011 at 20:22 | history | answered | Ian Martin | CC BY-SA 3.0 |