Abstract
Abstract
We determine the characteristic polynomials of the matrices
$[q^{\,j-k}+t]_{1\le \,j,k\le n}$
and
$[q^{\,j+k}+t]_{1\le \,j,k\le n}$
for any complex number
$q\not =0,1$
. As an application, for complex numbers
$a,b,c$
with
$b\not =0$
and
$a^2\not =4b$
, and the sequence
$(w_m)_{m\in \mathbb Z}$
with
$w_{m+1}=aw_m-bw_{m-1}$
for all
$m\in \mathbb Z$
, we determine the exact value of
$\det [w_{\,j-k}+c\delta _{jk}]_{1\le \,j,k\le n}$
.
Publisher
Cambridge University Press (CUP)
Reference5 articles.
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