TY - JOUR

T1 - The generalized matrix sector function and the separation of matrix eigenvalues

AU - Shieh, Leangs S.

AU - Tsai, Jasons H.

AU - Yates, Robert E.

N1 - Funding Information:
This work was supported in part by the U.S. Army Research Office, under contract DAAG 29-83-K-0037, and U.S. Army Missile Command, under contract DAAH 01-85-C-A111.

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

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U2 - 10.1093/imamci/2.3.251

DO - 10.1093/imamci/2.3.251

M3 - Article

AN - SCOPUS:0040848583

VL - 2

SP - 251

EP - 258

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

SN - 0265-0754

IS - 3

ER -