Almost Hadamard Matrices: General Theory and Examples

Teodor Banica, Ion Nechita, Karol Życzkowski
2012 Open systems & information dynamics  
We develop a general theory of "almost Hadamard matrices". These are by definition the matrices H ∈ M N (R) having the property that U = H/ √ N is orthogonal, and is a local maximum of the 1-norm on O(N ). Our study includes a detailed discussion of the circulant case (H ij = γ j−i ) and of the two-entry case (H ij ∈ {x, y}), with the construction of several families of examples, and some 1-norm computations. 2000 Mathematics Subject Classification. 05B20 (15B10).
doi:10.1142/s1230161212500242 fatcat:nrr6aohgyrejjbya32iqg2spte