## Combined matrices of sign regular matrices.(English)Zbl 1334.15083

Summary: The combined matrix of a nonsingular matrix $$A$$ is the Hadamard (entry wise) product $$C(A) = A \circ(A^{- 1})^T$$. Since each row and column sum of $$C(A)$$ is equal to one, the combined matrix is doubly stochastic when it is nonnegative. In this work, we study the nonnegativity of the combined matrix of sign regular matrices, based upon their signature. In particular, a few coordinates of the signature $$\varepsilon$$ of $$A$$ play a crucial role in determining whether or not $$C(A)$$ is nonnegative.

### MSC:

 15B48 Positive matrices and their generalizations; cones of matrices 15B57 Hermitian, skew-Hermitian, and related matrices
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### References:

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