1. SPECTRAL STRUCTURES OF IRREDUCIBLE TOTALLY NONNEGATIVE MATRICES.
- Author
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Fallat, Shaun M., Gekhtman, Michael I., and Johnson, Charles R.
- Subjects
- *
GLOBAL analysis (Mathematics) , *NONNEGATIVE matrices , *JORDAN matrix , *EIGENVALUES , *ALGEBRA , *MATRICES (Mathematics) , *UNIVERSAL algebra , *MATHEMATICS - Abstract
An n-by-n matrix is called totally nonnegative if every minor of A is nonnegative. The problem of interest is to characterize all possible Jordan canonical forms (Jordan structures) of irreducible totally nonnegative matrices. We show that the positive eigenvalues of such matrices have algebraic multiplicity one, and also demonstrate key relationships between the number and sizes of the Jordan blocks corresponding to zero. These notions yield a complete description of all Jordan forms through n = 7, as well as numerous general results. We also define a notion of ‘principal rank’ and employ this idea throughout. [ABSTRACT FROM AUTHOR]
- Published
- 2000
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