Advances in Operator Theory

Almost Hadamard matrices with complex entries

Teodor Banica and Ion Nechita

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We discuss an extension of the almost Hadamard matrix formalism, to the case of complex matrices. Quite surprisingly, the situation here is very different from the one in the real case, and our conjectural conclusion is that there should be no such matrices, besides the usual Hadamard ones. We verify this conjecture in a number of situations, and notably for most of the known examples of real almost Hadamard matrices, and for some of their complex extensions. We discuss as well some potential applications of our conjecture, to the general study of complex Hadamard matrices.

Article information

Adv. Oper. Theory, Volume 3, Number 1 (2018), 137-177.

Received: 9 February 2017
Accepted: 12 May 2017
First available in Project Euclid: 5 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15B10: Orthogonal matrices
Secondary: 05B20: Matrices (incidence, Hadamard, etc.) 14P05: Real algebraic sets [See also 12D15, 13J30]

Hadamard matrix Fourier matrix unitary group


Banica, Teodor; Nechita, Ion. Almost Hadamard matrices with complex entries. Adv. Oper. Theory 3 (2018), no. 1, 137--177. doi:10.22034/aot.1702-1114.

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