Mathematics & Computer Science
Event Title
The Necessary and Sufficient Conditions to Form a Hadamard Submatrix from a Fourier Matrix
Document Type
Oral Presentation
Location
Indianapolis, IN
Start Date
13-4-2018 1:45 PM
End Date
13-4-2018 2:45 PM
Sponsor
John Herr (Butler University)
Description
A matrix is considered Hadamard if all of its entries are of unit modulus and the columns are mutually orthogonal. Fourier matrices, a subclass of the Hadamard matrices, contain entries of ordered roots of unity given as a function of the indices. In this talk, we formulate a conjecture for the necessary and sufficient conditions for the existence of a Hadamard submatrix of a Fourier matrix for a particular dimensions. We prove the nonexistence of a Hadamard submatrix for many cases.
The Necessary and Sufficient Conditions to Form a Hadamard Submatrix from a Fourier Matrix
Indianapolis, IN
A matrix is considered Hadamard if all of its entries are of unit modulus and the columns are mutually orthogonal. Fourier matrices, a subclass of the Hadamard matrices, contain entries of ordered roots of unity given as a function of the indices. In this talk, we formulate a conjecture for the necessary and sufficient conditions for the existence of a Hadamard submatrix of a Fourier matrix for a particular dimensions. We prove the nonexistence of a Hadamard submatrix for many cases.