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10 votes
3 answers
830 views

Find the inverse of a matrix that is very similar to the Hilbert matrix

The standard Hilbert matrix $H$ is given by $$H_{ij}=\frac{1}{i+j-1},$$ and it has an inverse given for example in this MO question. Now I have encountered a matrix $M$ of similar form, namely, $$...
5 votes
1 answer
199 views

Find the inverse of a more general matrix that is similar to the Hilbert matrix

In the last MO question , the following matrix is given: $$M_{ij}=\left[\frac{1+(-1)^{i+j}}{i+j-1}\right]$$ and its inverse has been discussed. Now the problem is further extended to a more general ...