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Palestra American Corner


Topics on the Nonnegative Inverse Eigenvalue Problem

Charles R. Johnson (College of William and Mary)
Palestra inserida na iniciativa “NOVA Online Distinguished Lecture Series on Mathematics”
Dia 26 Fev | 14h

About the speaker: Charles R. Johnson is an American mathematician specializing in Linear Algebra. He is a Class of 1961 Professor of Mathematics at College of William and Mary. He has authored or co-authored more than a dozen books, and three hundred papers in prestigious specialised journals. The books Matrix Analysis and Topics in Matrix Analysis, co-written by him with Roger Horn, are standard texts in advanced Linear Algebra.

Additional information: here

Abstract: As a practical matter, the very difficult nonnegative inverse eigenvalue Problem (NIEP) has become a bundle of more particular problems. We report on two of these: 1) The doubly stochastic single eigenvalue problem asks which individual complex numbers occur as an eigenvalue of a doubly stochastic matrix. This problem, first discussed in the 1960's, remains open, though its row stochastic analog enjoyed its first "solution" about 70 years ago and has received refinements since. We report on the intriguing progress that is partly empirical. 2) Spectra with repeated eigenvalues may be nonnegatively realizable with some Jordan structures and not others. We sort out what is currently known and what is likely true about the Jordan NIEP. 

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