Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602371 | Linear Algebra and its Applications | 2008 | 13 Pages |
Abstract
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 jth 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).
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