Rank-deficient submatrices of Kronecker products of Fourier matrices
نویسندگان
چکیده
منابع مشابه
Rank-deficient submatrices of Kronecker products of Fourier matrices
We provide a set of maximal rank-deficient submatrices of a Kronecker product of two matrices A ⊗ B, and in particular the Kronecker product of Fourier matrices F = Fn1 ⊗ . . . ⊗ Fnk . We show how in the latter case, maximal rank-deficient submatrices can be constructedas tilings of rank-one blocks. Such tilings exist for any subgroup of a suitable Abelian group associated to the matrix F . The...
متن کاملRank-deficient submatrices of Fourier matrices
We consider the maximal rank-deficient submatrices of Fourier matrices. We do this by considering a hierarchical subdivision of these matrices into low rank blocks. We also explore some connections with the FFT, and with an uncertainty principle for Fourier transforms over finite Abelian groups.
متن کاملPermutation Equivalence Classes of Kronecker Products of Unitary Fourier Matrices
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many problems of mathematics and thoretical physics. The main result of the paper is splitting the set of all kronecker products of unitary Fourier matrices into pe...
متن کاملReconstruction of matrices from submatrices
For an arbitrary matrix A of n×n symbols, consider its submatrices of size k×k, obtained by deleting n−k rows and n−k columns. Optionally, the deleted rows and columns can be selected symmetrically or independently. We consider the problem of whether these multisets determine matrix A. Following the ideas of Krasikov and Roditty in the reconstruction of sequences from subsequences, we replace t...
متن کاملVisualizing Rank Deficient Models: A Row Equation Geometry of Rank Deficient Matrices and Constrained-Regression
Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.05.009