## Abstract

The matrix sector function of A is introduced and generalized to the matrix sector function of g(A), where the complex matrix A may have a real or complex characteristic polynomial and g(A) is a matrix function of a conformal mapping. The generalized matrix sector function of A is employed to separate the matrix eigenvalues relative to a sector, a circle, and a sector of a circle in the complex plane without actually seeking the characteristic polynomial and the matrix eigenvalues relative to a sector, a circle, and a sector of a circle in the complex plane without actually seeking the characteristic polynomial and the matrix eigenvalues themselves. Also, the generalized matrix sector function of A is utilized to carry out the block-diagonalization and block-triangularization of a system matrix, which are useful in developing applications to mathematical science and control-system problems.

Original language | English |
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Pages (from-to) | 251-258 |

Number of pages | 8 |

Journal | IMA Journal of Mathematical Control and Information |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1985 Dec 1 |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Control and Optimization
- Applied Mathematics