Abstract:
A doubly stochastic matrix is a square matrix
A = (aij ) of non-negative real numbers such that P
i
aij =
P
j
aij = 1.
The Chebyshev polynomial of the first kind is defined by the recur-
rence relation T0(x) = 1, T1(x) = x, and
Tn+1(x) = 2xTn(x) − Tn−1(x).
In this paper, we show a 2
k × 2
k
(for each integer k > 1) doubly
stochastic matrix whose characteristic polynomial is x
2 − 1 times
a product of irreducible Chebyshev polynomials of the first kind
(upto rescaling by rational numbers).
