Timeline for sign of values of an integer polynomial on roots of unity
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jan 21, 2011 at 15:38 | comment | added | Luis H Gallardo |
@unknown mannekin pisse: Assume that $C$ is also a Hadamard matrix. I am afraid not to yet understand why when the circulant matrix $C$ is symmetric or close to be symmetric, the associated quadratic form $Q$ transforming $x \to x^T Cx$ (or something alike when $C$ is not symmetric) must have a very special signature, of the type $(1,*)$ or $(-1,*)$, (that forces $n=4$) while normally (for more non-circulant Hadamard's) the signature should be of the type $ ((n+\sqrt{n})/2,(n-\sqrt{n})/2)$.
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| Jan 6, 2011 at 10:13 | comment | added | Luis H Gallardo | Let $C=circ(r_0,r_1, \ldots ,r_{n-1})$ be the circulant matrix with first row $r_0, \ldots ,r_{n-1}$. The $R(\omega)$ are the eigenvalues of $C$. We may consider the special case when $C$ is orthogonal in order to see different signs taken by the eigenvalues. | |
| Dec 30, 2010 at 22:18 | vote | accept | Luis H Gallardo | ||
| Dec 30, 2010 at 22:16 | history | edited | user631 | CC BY-SA 2.5 |
added 417 characters in body
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| Dec 30, 2010 at 21:51 | history | answered | user631 | CC BY-SA 2.5 |