Schur decompositions of a matrix and the boundary of its pseudospectrum

Lyonell Boulton, Peter Lancaster

Research output: Contribution to journalArticlepeer-review


We discuss the notion of irreducible block Schur decomposition of a complex square matrix and show how such a decomposition provides information about singularities in the boundaries of pseudospectra of the matrix. Detailed examples are provided to illustrate the theory. © 2010 Society for Industrial and Applied Mathematics.

Original languageEnglish
Pages (from-to)2921-2933
Number of pages13
JournalSIAM Journal on Matrix Analysis and Applications
Issue number5
Publication statusPublished - 2010


  • Irreducible block Schur decomposition
  • Path-following algorithms
  • Pseudospectra of linear transformations
  • Schur triangular form


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