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