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If $S$ is a non singular symmetric matrix over a number field and $D_k$ is its principal minor of order $k$, is $\frac{D_k}{D_{k-1}} > 0$ always true?

By ExtraProxies | Proxy Quality | Comments are Closed | 12 February, 2018 | 0

In “The Theory of Matrices” by Gantmacher, Chapter II, section 4: Corollary $ 3$ : If $ S= ||s_{ik}||_1^n$ is a symmetric matrix of rank $ r$ and $ $ D_k= S\bigl( \begin{smallmatrix} 1 & 2 & \dots & k \ 1 & 2 & \dots & k \end{smallmatrix} \bigr)\ne 0 \ \ \ \Read more

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If $S$ is a non singular symmetric matrix over a number field and $D_k$ is its principal minor of order $k$, is $\frac{D_k}{D_{k-1}} > 0$ always true?

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