In contrast to SPD matrices, few tools exist perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built as quotient affine-invariant by congruence action positive diagonal space matrices had always been thought a homogeneous space. contrast, we view in this work Lie group and left-invariant metric. This unexpected new vie...

The notion of finite zeros of continuous-time positive linear systems is introduced. It is shown that such zeros are real numbers. It is also shown that a square positive strictly proper or proper system of uniform rank with observability matrix of full column rank has no finite zeros. The problem of zeroing the system output for positive systems is defined. It is shown that a square positive s...

Recently, this journal has published a paper which dealt with basis expansion model (BEM) based least-squares (LS) channel estimation in doubly-selective orthogonal frequency-division multiplexing (DS-OFDM) systems. The least-squares channel estimator computes the pseudo-inverse of a channel estimation matrix. For the existence of the pseudo-inverse, it is necessary that the channel estimation ...

Let q be an algebraic integer of degree d ≥ 2. Consider the rank of the multiplicative subgroup of C generated by the conjugates of q. We say q is of full rank if either the rank is d− 1 and q has norm±1, or the rank is d. In this paper we study some properties of Z[q] where q is an algebraic integer of full rank. The special cases of when q is a Pisot number and when q is a Pisot-cyclotomic nu...