Noncirculant Toeplitz matrices all of whose powers are Toeplitz

Griffin, Kent, Stuart, Jeffrey L., and Tsatsomeros, Michael J.. "Noncirculant Toeplitz matrices all of whose powers are Toeplitz." Czechoslovak Mathematical Journal 58.4 (2008): 1185-1193. <http://eudml.org/doc/37895>.

@article{Griffin2008,
abstract = {Let $a$, $b$ and $c$ be fixed complex numbers. Let $M_n(a,b,c)$ be the $n\times n$ Toeplitz matrix all of whose entries above the diagonal are $a$, all of whose entries below the diagonal are $b$, and all of whose entries on the diagonal are $c$. For $1\le k\le n$, each $k\times k$ principal minor of $M_n(a,b,c)$ has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of $M_n(a,b,c)$. We also show that all complex polynomials in $M_n(a,b,c)$ are Toeplitz matrices. In particular, the inverse of $M_n(a,b,c)$ is a Toeplitz matrix when it exists.},
author = {Griffin, Kent, Stuart, Jeffrey L., Tsatsomeros, Michael J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Toeplitz matrix; Toeplitz inverse; Toeplitz powers; principal minor; Fibonacci sequence; Toeplitz matrix; Toeplitz inverse; Toeplitz powers; principal minor; Fibonacci sequence},
language = {eng},
number = {4},
pages = {1185-1193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Noncirculant Toeplitz matrices all of whose powers are Toeplitz},
url = {http://eudml.org/doc/37895},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Griffin, Kent
AU - Stuart, Jeffrey L.
AU - Tsatsomeros, Michael J.
TI - Noncirculant Toeplitz matrices all of whose powers are Toeplitz
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1185
EP - 1193
AB - Let $a$, $b$ and $c$ be fixed complex numbers. Let $M_n(a,b,c)$ be the $n\times n$ Toeplitz matrix all of whose entries above the diagonal are $a$, all of whose entries below the diagonal are $b$, and all of whose entries on the diagonal are $c$. For $1\le k\le n$, each $k\times k$ principal minor of $M_n(a,b,c)$ has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of $M_n(a,b,c)$. We also show that all complex polynomials in $M_n(a,b,c)$ are Toeplitz matrices. In particular, the inverse of $M_n(a,b,c)$ is a Toeplitz matrix when it exists.
LA - eng
KW - Toeplitz matrix; Toeplitz inverse; Toeplitz powers; principal minor; Fibonacci sequence; Toeplitz matrix; Toeplitz inverse; Toeplitz powers; principal minor; Fibonacci sequence
UR - http://eudml.org/doc/37895
ER -