Article ID Journal Published Year Pages File Type
4602371 Linear Algebra and its Applications 2008 13 Pages PDF
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).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory