Title :
Eigenvalues of symmetric matrices: System theory conditions for distinctness
Author :
Dickinson, Bradley W. ; Steiglitz, Kenneth
Author_Institution :
Princeton University, Princeton, NJ, USA
fDate :
4/1/1980 12:00:00 AM
Abstract :
We derive the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas. We then give a sufficient condition for distinctness of eigenvalues based on the minimality of an associated linear system.
Keywords :
Controllability; Eigenvalues; Linear systems, time-invariant continuous-time; Matrices; Observability; Controllability; Eigenvalues and eigenfunctions; Linear matrix inequalities; Linear systems; Observability; Polynomials; Sufficient conditions; Symmetric matrices;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1980.1102293
