vol11_pp281-291. 139KB Jun 04 2011 12:05:52 AM
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It is shown that if the connected graph of the specified entries of a combinatorially symmetric, partial totally positive matrix is monotonically labeled block clique, then there is
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N -square complex matrix with prescribed diagonal entries and prescribed eigenvalues.. A
They introduced the terms “essentially nonnegative matrix” for matrices whose off-diagonal elements are nonnegative and “essentially positive matrix” for essentially
Of particular interest is the connection between this standard inverse eigenvalue problem and describing all the possible associated ordered multiplicity lists, along with
In this section we extend the results of Section 2 for idempotent matrices of the form (2.2) for some Schur complements with zero diagonal entries.. We start with the following
In the context of invertible M-matrices (i.e., when B ≥ 0), condition (ii) of Theorem 4.3 is associated with diagonal dominance of AD because the diagonal entries are positive and
In this note, we generalize the explicit formulae in [5] for the polar factors of nonsingular real square matrices of order 2, and obtain explicit formulae for polar factors of n − by
Also, it is known (see [3]) that any product of n − 1 fully indecomposable stochastic matrices of order n must have all positive entries, so the problem may be restricted to the
