how to prove an n*n matrix defined by Aij=1/(i+j-1) is a positive define matrix?
i've tried to calculate the principal minors of A, but it seems not working
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1This is known as the Hilbert matrix. If you search for its name, I suspect that you’ll find a proof fairly quickly. – Ben Grossmann Apr 20 '22 at 14:20
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Apr 20 '22 at 14:23
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@Ben Ok, thank you. – Andy Tao Apr 20 '22 at 14:29
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In particular, my proof here shows that the matrix is positive definite (in order to show that the matrix is invertible). – Ben Grossmann Apr 20 '22 at 14:45
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@Ben Thank you so much for your help. You have solved my problem. – Andy Tao Apr 21 '22 at 04:17
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@Dietrich Yes, it does. Thanks. – Andy Tao Apr 21 '22 at 04:18
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@Oliver Yes, it does. Thanks. – Andy Tao Apr 21 '22 at 04:18