5 problems

Let $U\in\sqrt{N}U_N$ be a rescaled unitary matrix. A strict almost Hadamard matrix, an isolated complex Hadamard matrix, and a complex Hadamard matrix with minimal AHM/CHM defect…

Let $q\geq3$ be prime, let $K\in M_{M\times N}(\mathbb C)$ be an isolated truncation of $F_p$ with $p$ prime, and let $S,T$ be the sets used in Theorem 4.4. That theorem constructs…

A square master Hadamard matrix is a master Hadamard matrix of square size, and $F_p$ denotes the Fourier matrix of prime order $p$. A matrix is isolated when it has no nontrivial…

Let $H\in M_{M\times N}(\mathbb C)$ be a dephased partial Hadamard matrix. It is regular when its row scalar products decompose as sums of cycles, isolated when it has only trivial…

Let $F_{S,p}$ denote the partial Fourier matrix associated to a subset $S\subset\mathbb Z_p$, where $p$ is prime. Truncation conjecture. There exists a constant $\varepsilon>0$ suc…