Eigenvalues of matrices with a given graph
 
 
Description:  Given a graph G on n vertices the generalized inverse eigenvalue problem for G consists in describing the all the possible sequences of 2n-1 real numbers such that there exists a real matrix symmetric matrix A whose graph is G, whose eigenvalues are the first n elements of the sequence and such that the the last n-1 numbers of the sequence are the eigenvalues of A(v) (the submatrix obtained from by deleting the row and column v). The interlacing inequalities between the last n-1 numbers of a given sequence and the first n numbers provide a necesasry condition for the existence of such matrix. Using the implicit function theorem we will show that strict interlacing inequalities are sufficient for the existence of such a matrix. These strict interlacing are necessary just for one graph: the path (M. Fiedler, 1969)
Area(s):
Date:  2007-12-12
Start Time:   14:30
Speaker:  António Leal Duarte (CMUC/Mat. FCTUC)
Place:  5.5
Research Groups: -Algebra and Combinatorics
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