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Block Toeplitz Matrices

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

Abstract

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
$$ A = \left( {\begin{array}{*{20}{c}} {{a_0}}{{a_{ - 1}}}{{a_{ - 2}}} \cdots \\ {{a_1}}{{a_0}}{{a_{ - 1}}} \cdots \\ {{a_2}}{{a_1}}{{a_0}} \cdots \\ \cdots \cdots \cdots \cdots \end{array}} \right) $$
(6.1)
where \(\{ a_k \} _{k \in z} \) is a sequence of N × N matrices,\( {a_k} \in B({C^N}) \) for all k ∈ Z.

Keywords

Matrix Function Toeplitz Operator Scalar Case Toeplitz Matrix Toeplitz Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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