@article{Morillas_2021, title={Dual finite frames for vector spaces over an arbitrary field with applications}, volume={13}, url={http://armjmath.sci.am/index.php/ajm/article/view/479}, DOI={10.52737/18291163-2021.13.2-1}, abstractNote={<p>In the present paper, we study frames for finite-dimensional vector spaces over an arbitrary field. We develop a theory of dual frames in order to obtain and study the different representations of the elements of the vector space provided by a frame. We relate the introduced theory with the classical one of dual frames for Hilbert spaces and apply it to study dual frames for three types of vector spaces: for vector spaces over conjugate closed subfields of the complex numbers (in particular, for cyclotomic fields), for metric vector spaces, and for ultrametric normed vector spaces over complete non-archimedean valued fields. Finally, we consider the matrix representation of operators using dual frames and its application to the solution of operators equations in a Petrov-Galerkin scheme.</p>}, number={2}, journal={Armenian Journal of Mathematics}, author={Morillas, Patricia Mariela}, year={2021}, month={May}, pages={1–36} }