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University of Regina Department of Mathematics and Statistics

University of Regina
Department of Mathematics and Statistics
Speaker: Shaun Fallat (University of Regina)
Title: Sign Variation of Vectors and Eigenvalues of Oscillatory Matrices
Time & Place: Friday, September 18, 3:15 - 4:15 pm, CL 435
In 1930, I. Schoenberg proved the seminal result that, as a linear transfor-
mation, a totally positive matrix cannot increase the number of sign changes
in a vector. In fact, the transformations that cannot increase the number
of sign variations are of interest in a variety of applications, including ap-
proximation theory and shape preserving functions.
Around the same time, but from a different perspective, Gantmacher and
Krein proved that the eigenvalues of an oscillatory matrix are positive and
all distinct. In addition, though often less advertised, they proved a num-
ber of interesting properties about the associated eigenvectors of oscillatory
In this talk, I will review the above facts, and establish a connection
between them culminating in a new, more comprehensive, characterization
of the spectral structure of oscillatory matrices.


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics