The 
tridiagonal
matrix (also called the Clement matrix) defined by
![S_n=[0 n 0 0 ... 0; 1 0 n-1 0 ... 0; 0 2 0 n-2 ... 0; | | ... ... ... |; 0 0 0 n-1 0 1; 0 0 0 0 n 0].](/images/equations/KacMatrix/NumberedEquation1.svg) |
The eigenvalues are 
for 
, 1, ..., 
.
Kac Matrix
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Cite this as:
Weisstein, Eric W. "Kac Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KacMatrix.html