On the Inverse Eigenvalue Problem for Irreducible Doubly Stochastic Matrices of Small Orders
2014
The inverse eigenvalue problem is a classical and difficult
problem in matrix theory. In the case of real spectrum, we first present some sufficient
conditions of a real r-tuple (for ; 3; 4; 5) to be realized by a
symmetric stochastic matrix. Part of these conditions is also extended
to the complex case in the case of complex spectrum where the realization matrix may not
necessarily be symmetry. The main approach throughout the paper in
our discussion is the specific construction of realization matrices and the
recursion when the targeted r-tuple is updated to a -tuple.
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