Weaving Riesz Bases

This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is both necessary and sufficient for vector reconstruction, which is applicable to Fourier matrices. Furthermore, we show that these characterizations are still valid in the infinite dimensional case, for Riesz bases. Finally, we obtain several results for weaving Riesz bases of translations.