User user15871

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Oct 3, 2021 at 20:51

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Oct 15, 2015 at 10:23

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Student

Jun 18, 2011 at 20:50

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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 $i\neq j$?

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 20:40

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Scholar

Jun 18, 2011 at 20:35

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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 $i\neq j$?

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 20:33

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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 $i\neq j$?

Jun 18, 2011 at 20:30

asked

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 $i\neq j$?

Jun 18, 2011 at 19:42

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