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Noncirculant Toeplitz matrices all of whose powers are Toeplitz

Kent GriffinJeffrey L. StuartMichael J. Tsatsomeros — 2008

Czechoslovak Mathematical Journal

Let a , b and c be fixed complex numbers. Let M n ( a , b , c ) be the n × 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 k n , each k × 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...

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