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IMA Journal of Mathematical Control and Information 1985 2(3):251-258; doi:10.1093/imamci/2.3.251
© 1985 by Institute of Mathematics and its Applications
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The Generalized Matrix Sector Function and the Separation of Matrix Eigenvalues

LEANGS S. SHIEH, JASONS. H. TSAI and ROBERT E. YATES

Department of Electrical Engineering, University of Houston-University Park Houston, Texas, 77004 U.S.A.
The Guidance and Control Directorate, U.S. Army Missile Command Redstone, AL 35809, U.S.A.

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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