Displaying similar documents to “An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries.”

Companion matrices and their relations to Toeplitz and Hankel matrices

Yousong Luo, Robin Hill (2015)

Special Matrices

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In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices,...

Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

A.K. Abdikalykov, V.N. Chugunov, Kh.D. Ikramov (2015)

Special Matrices

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Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

Noncirculant Toeplitz matrices all of whose powers are Toeplitz

Kent Griffin, Jeffrey L. Stuart, Michael J. Tsatsomeros (2008)

Czechoslovak Mathematical Journal

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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...

On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications

A. Ohashi, T. Sogabe, T.S. Usuda (2015)

Special Matrices

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We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.