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Results tagged with eigenvalues
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user 48831
eigenvalues of matrices or operators
7
votes
Eigenvalues of a matrix with entries involving combinatorics
out that it suffices to show that
the $(n-1)\times (n-1)$ submatrix $L(n,\ell)$ with coefficients
$$L_{i,j}(n,\ell)=[t^{\ell j-i}] \left(\frac{1-t^\ell}{1-t}\right)^n,\,\;\;\;1\leq i,j \leq n-1$$
has eigenvalues … Holte proved that $P(n,\ell)$ has eigenvalues $1,\ell^{-1},\ldots,\ell^{-(n-1)}$,
that the eigenvectors do not depend on the base $\ell$, and described the left and right eigenvectors explicitly. …
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