Open AccessABOUT THE SYSTEMS WITH FULL SPARK
Author(s) -
Д. А. Рогач,
Д. А. Рогач
Publication year - 2019
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2019-25-4-29-35
Subject(s) - completeness (order theory) , spark (programming language) , unitary state , fourier transform , dimension (graph theory) , euclidean space , euclidean geometry , mathematics , linear system , property (philosophy) , phase space , algebra over a field , pure mathematics , computer science , algorithm , mathematical analysis , geometry , physics , philosophy , epistemology , political science , law , programming language , thermodynamics
Frames of a finite-dimensional Euclidean and unitary spaces composed of discrete Fourier transform matrices are considered. The relationship of phaseless reconstruction systems with the alternative completeness property is presented. In the complex case, alternative completeness is only a necessary condition for phaseless reconstruction. A system of vectors is constructed such that each of its subsystems with a volume equal to the dimension of space is linearly independent. These systems are called systems with full spark. In particular, such systems are optimal for phase retrieval.