## 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.