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Kac Matrix

The $(n+1)\times(n+1)$ Tridiagonal Matrix (also called the Clement Matrix) defined by

\begin{displaymath}
S_n=\left[{\matrix{
0 & n & 0 & 0 & \cdots & 0\cr
1 & 0 & ...
...0 & 0 & 0 & n-1 & 0 & 1\cr
0 & 0 & 0 & 0 & n & 0\cr}}\right].
\end{displaymath}

The Eigenvalues are $2k-n$ for $k=0$, 1, ..., $n$.




© 1996-9 Eric W. Weisstein
1999-05-26