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Results tagged with eigenvalues
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user 135311
eigenvalues of matrices or operators
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Generalization of Cauchy's eigenvalue interlacing theorem?
Cauchy's Interlacing Theorem says that given an $n \times n$ symmetric matrix $A$, let $B$ be an $(n-1) \times (n-1)$ principal submatrix of it, then the eigenvalues of $A$ and those of $B$ interlace. … For example, let $$A=\begin{bmatrix}
0 & 1 & 1 & 0\\
1 & 0 & 0 & 1\\
1 & 0 & 0 & 1\\
0 & 1 & 1 & 0
\end{bmatrix}$$
The eigenvalues of $A$ are $2, 0, 0, -2$. …
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