Timeline for structure of singular matrices whose entries have modulus one
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2010 at 10:24 | vote | accept | Vagabond | ||
| Oct 9, 2010 at 10:22 | comment | added | Vagabond | Yes, so that settles it. I realise one can pose it as a problem of linkage, if 4 rods are linked to form a quadrilateral then its not rigid so there would be a lot of solution. The question about when the matrix is further assumed to be generalized vandermonde type under the hypotheses that all entries has to be algebraic integers is what I need, I guess I should pose it as a separate question but I will try some more before that. | |
| Oct 9, 2010 at 9:00 | comment | added | Denis Serre | Right. But, as I evoqued in my answer, the construction as a lot of flexibility. Actually, there is a full open set in the parameter set for which the construction works. | |
| Oct 9, 2010 at 8:08 | comment | added | Vagabond | The $N$ you took if you eliminate the first row and column we get [-1 1; 1 -1] which is singular and we have the condition that none of the sub matrices are singular. I am not sure though if that affects the rest of the construction. | |
| Oct 9, 2010 at 7:00 | comment | added | Denis Serre | I make a correcion, because I forgot a factor $i$ in $N^{-1}e$. This does not change the rest. | |
| Oct 9, 2010 at 6:59 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Oct 8, 2010 at 19:48 | history | edited | Denis Serre | CC BY-SA 2.5 |
An example of singular $A$ for $n=4$.
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| Oct 8, 2010 at 18:23 | comment | added | Vagabond | How do we proceed from here ? I would be eagerly waiting for the rest of the argument. | |
| Oct 8, 2010 at 18:01 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Oct 8, 2010 at 18:00 | comment | added | Denis Serre | Correct! I wanted to write $\hat M$. I make the correction immediately. | |
| Oct 8, 2010 at 17:09 | comment | added | Vagabond | When I do what you suggested I get $e^T M^{-1} e = 1$ | |
| Oct 8, 2010 at 16:10 | history | answered | Denis Serre | CC BY-SA 2.5 |