Related papers: Circulant conference matrices for new complex Hada…
In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
Reformulation of a combinatorial problem into optimization of a statistical-mechanics system, enables finding a better solution using heuristics derived from a physical process, such as by the SA (Simulated Annealing). In this paper, we…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are…
Many interesting examples of complex Hadamard matrices $H\in M_N(\mathbb C)$ can be put, up to the standard equivalence relation for such matrices, in bistochastic form. We discuss here this phenomenon, with a number of computations for…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard…
A complex Hadamard matrix is a square matrix W with complex entries of absolute value 1 satisfying WW*=nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we give constructions of complex…
A Hadamard matrix is a scaled orthogonal matrix with $\pm 1$ entries. Such matrices exist in certain dimensions: the Hadamard conjecture is that such a matrix always exists when $n$ is a multiple of 4. A conjecture attributed to Ryser is…
We construct new pairs of orthogonal maximal abelian $*$-subalgebras of $M_6(\mathbb C)$, by classifying all self-adjoint complex Hadamard matrices of order 6. In particular, we exhibit a non-affine one-parameter family of non-equivalent…
We have extended the Paley constructions for Hadamard matrices and obtained some series of Hadamard matrices. Especially Paley construction-II is applicable for odd prime power q is congruent to 1(mod 4) however our method is applicable for…
Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than $0$. It is shown that unitary…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
The collection of cyclic Hadamard matrices {H = (a_{i - j}) : 0 <= i, j < n, and a_i = -1, 1} of order n is characterized by the orthogonality relation HH^T = nI. Only two of such matrices are currently known. It will be shown that this…
Cretan matrices are orthogonal matrices with elements $\leq 1$. These may have application in forming some new materials. There is a search for Cretan matrices, especially with high determinant, for all orders. These have been found by both…
Hadamard matrices are $(-1, +1)$ square matrices with mutually orthogonal rows. The Hadamard conjecture states that Hadamard matrices of order $n$ exist whenever $n$ is $1$, $2$, or a multiple of $4$. However, no construction is known that…
We present a new method for constructing affine families of complex Hadamard matrices in every even dimension. This method has an intersection with the Di\c{t}\u{a} construction and it generalizes the Sz\"oll\H{o}si's method. We reproduce…
A new type of complex Hadamard matrices of order 9 are constructed. The studied matrices are symmetric, block circulant with circulant blocks ($BCCB$) and form an until now unknown non-reducible and non-affine two-parameter orbit. Several…
The optimal branch number of MDS matrices has established their importance in designing diffusion layers for various block ciphers and hash functions. As a result, numerous matrix structures, including Hadamard and circulant matrices, have…