The generalized matrix sector function and the separation of matrix eigenvalues

Leangs S. Shieh, Jasons H. Tsai, Robert E. Yates

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)251-258
Number of pages8
JournalIMA Journal of Mathematical Control and Information
Volume2
Issue number3
DOIs
Publication statusPublished - 1985 Dec 1

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Applied Mathematics

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