BCCB complex Hadamard matrices of order 9, and MUBs
نویسندگان
چکیده
منابع مشابه
Parametrizing complex Hadamard matrices
Abstract. The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N ≥ 4 admits an affine orbit. This settles a recent open problem of Tadej and Życzkowski [11], who asked whether a real Hadamard matrix can be isolated among complex ones. In particular, we apply our construction...
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What is the dimension of a smooth family of complex Hadamard matrices including the Fourier matrix? We address this problem with a power series expansion. Studying all dimensions up to 100 we find that the first order result is misleading unless the dimension is 6, or a power of a prime. In general the answer depends critically on the prime number decomposition of the dimension. Our results sug...
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A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c 6= 1 to obtain another complex Hadamard matrix. We give a characterisation of rectang...
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Two Hadamard matrices of order 764 of Goethals– Seidel type are constructed. Recall that a Hadamard matrix of order m is a {±1}-matrix A of size m × m such that AA T = mI m , where T denotes the transpose and I m the identity matrix. We refer the reader to one of [2, 4] for the survey of known results about Hadamard matrices. In our previous note [1], written about 13 years ago, we listed 17 in...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.04.012