@article{dopico_koev_2008, title={Bidiagonal decompositions of oscillating systems of vectors}, volume={428}, ISSN={["0024-3795"]}, DOI={10.1016/j.laa.2007.12.002}, abstractNote={We establish necessary and sufficient conditions, in the language of bidiagonal decompositions, for a matrix V to be an eigenvector matrix of a totally positive matrix. Namely, this is the case if and only if V and V - T are lowerly totally positive. These conditions translate into easy positivity requirements on the parameters in the bidiagonal decompositions of V and V - T . Using these decompositions we give elementary proofs of the oscillating properties of V . In particular, the fact that the j th column of V has j - 1 changes of sign. Our new results include the fact that the Q matrix in a QR decomposition of a totally positive matrix belongs to the above class (and thus has the same oscillating properties).}, number={11-12}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Dopico, Froilan M. and Koev, Plamen}, year={2008}, month={Jun}, pages={2536–2548} }
 @article{canto_koev_ricarte_urbano_2008, title={LDU FACTORIZATION OF NONSINGULAR TOTALLY NONPOSITIVE MATRICES}, volume={30}, ISSN={["1095-7162"]}, DOI={10.1137/060662897}, abstractNote={An $n \times n$ real matrix $A$ is said to be (totally negative) totally nonpositive if every minor is (negative) nonpositive. In this paper, we study the properties of a totally nonpositive matrix and characterize the case of a nonsingular totally nonpositive matrix $A$, with $a_{11}< 0$ in terms of its $LDU$ factorization ($L(U)$) is a unit lower- (upper-) triangular matrix, respectively, and $D$ is a diagonal matrix). This characterization allows us to significantly reduce the number of minors to be checked in order to decide the total nonpositivity of a nonsingular matrix with a negative (1,1) entry.}, number={2}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Canto, Rafael and Koev, Plamen and Ricarte, Beatriz and Urbano, Ana M.}, year={2008}, pages={777–782} }