کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599506 | 1631136 | 2014 | 25 صفحه PDF | دانلود رایگان |
We explicitly determine the skew-symmetric eigenvectors and corresponding eigenvalues of the real symmetric Toeplitz matricesT=T(a,b,n):=(a+b|j−k|)1≤j,k≤nT=T(a,b,n):=(a+b|j−k|)1≤j,k≤n of order n≥3n≥3 where a,b∈Ra,b∈R, b≠0b≠0. The matrix T is singular if and only if c:=ab=−n−12. In this case we also explicitly determine the symmetric eigenvectors and corresponding eigenvalues of T. If T is regular, we explicitly compute the inverse T−1T−1, the determinant detTdetT, and the symmetric eigenvectors and corresponding eigenvalues of T are described in terms of the roots of the real self-inversive polynomial pn(δ;z):=(zn+1−δzn−δz+1)/(z+1)pn(δ;z):=(zn+1−δzn−δz+1)/(z+1) if n is even, and pn(δ;z):=zn+1−δzn−δz+1pn(δ;z):=zn+1−δzn−δz+1 if n is odd, δ:=1+2/(2c+n−1)δ:=1+2/(2c+n−1).
Journal: Linear Algebra and its Applications - Volume 459, 15 October 2014, Pages 595–619