Geodesic
Noncirculant Toeplitz matrices all of whose powers are Toeplitz
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1185-1193 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $1\leq k\leq n$, 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.
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 $1\leq k\leq n$, 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.
Classification : 11B37, 11B39, 15A15, 15A57
Keywords: Toeplitz matrix; Toeplitz inverse; Toeplitz powers; principal minor; Fibonacci sequence 
@article{CMJ_2008_58_4_a22,
     author = {Griffin, Kent and Stuart, Jeffrey L. and Tsatsomeros, Michael J.},
     title = {Noncirculant {Toeplitz} matrices all of whose powers are {Toeplitz}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1185--1193},
     year = {2008},
     volume = {58},
     number = {4},
     mrnumber = {2471175},
     zbl = {1174.15011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a22/}
}
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Griffin, Kent; Stuart, Jeffrey L.; Tsatsomeros, Michael J. Noncirculant Toeplitz matrices all of whose powers are Toeplitz. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1185-1193. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a22/