|
|
|
|
|
|
|
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: |
|
| Start Time: |
14:30 |
|
Speaker: |
António Leal Duarte (CMUC/Mat. FCTUC)
|
|
Place: |
5.5
|
| Research Groups: |
-Algebra and Combinatorics
|
|
See more:
|
<Main>
|
|
| |
|
|
|
|
|
|
|
|
|
