Abstract
The combined matrix of a nonsingular matrix A is the Hadamard (entrywise) product . This paper deals with the characterization of the diagonal entries of a combined matrix C(A) of a given nonsingular real matrix A. A partial answer describing the diagonal entries of C(A) in the positive definite case was given by Fiedler in 1964. Recently in 2011, Fiedler and Markham characterized the sequence of diagonal entries of the combined matrix C(A) for any totally positive matrix A when the size is 3. For this case, we characterize totally negative matrices and we find necessary and sufficient conditions for the sequence of diagonal entries of C(A), in both cases, symmetric and nonsymmetric.
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