Automorphisms of generalized Sylvester Hadamard matrices

On Permanents of Sylvester Hadamard Matrices

It is well-known that a Sylvester Hadamard matrix can be described by means of a cocycle. In this paper it is shown that the additional internal structure in a Sylvester Hadamard matrix, provided by the cocycle, is su cient to guarantee some kind of reduction in the computational complexity of calculating its permanent using Ryser's formula. A Hadamard matrix H of order n is an n× n matrix with...

Complex Hadamard Matrices from Sylvester Inverse Orthogonal Matrices

A novel method to obtain parameterizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into...

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

On Eigenvalues of Row-Inverted Sylvester Hadamard Matrices

In this paper, the eigenvalues of row-inverted 2 × 2 Sylvester Hadamard matrices are derived. Especially when the sign of a single row or two rows of a 2×2 Sylvester Hadamard matrix are inverted, its eigenvalues are completely evaluated. As an example, we completely list all the eigenvalues of 256 different row-inverted Sylvester Hadamard matrices of size 8. Mathematics Subject Classification (...

Quasi-Cyclic Generalized Hadamard Matrices

In this paper, we define quasi-cyclic(QC) generalized Hadamard matrices and balanced QC generalized Hadamard matrices. Then we propose a new construction method for QC generalized Hadamard matrices. The proposed matrices are constructed from the balanced optimal low correlation zone(LCZ) sequence set which has correlation value −1 within low correlation zone.