Block Toeplitz Matrices

  • Albrecht Böttcher
  • Bernd Silbermann
Part of the Universitext book series (UTX)


A Toeplitz matrix is constant along the parallels to the main diagonal. Matrices whose entries in the parallels to the main diagonal form periodic sequences (with the same period N) are referred to as block Toeplitz matrices. Equivalently, A is a block Toeplitz matrix if and only if
$$ A = \left( {\begin{array}{*{20}{c}} {{a_0}}{{a_{ - 1}}}{{a_{ - 2}}} \cdots \\ {{a_1}}{{a_0}}{{a_{ - 1}}} \cdots \\ {{a_2}}{{a_1}}{{a_0}} \cdots \\ \cdots \cdots \cdots \cdots \end{array}} \right) $$
where \(\{ a_k \} _{k \in z} \) is a sequence of N × N matrices,\( {a_k} \in B({C^N}) \) for all k ∈ Z.


Matrix Function Toeplitz Operator Scalar Case Toeplitz Matrix Toeplitz Matrice 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  • Bernd Silbermann
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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