Hadamard Matrices and Their Applications
A. S. Hedayat,W. D. Wallis +1 more
TLDR
Hadamard matrices have been widely studied in the literature and many of their applications can be found in this paper, e.g., incomplete block designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III (SRSIII), optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects.Abstract:
An $n \times n$ matrix $H$ with all its entries $+1$ and $-1$ is Hadamard if $HH' = nI$. It is well known that $n$ must be 1, 2 or a multiple of 4 for such a matrix to exist, but is not known whether Hadamard matrices exist for every $n$ which is a multiple of 4. The smallest order for which a Hadamard matrix has not been constructed is (as of 1977) 268. Research in the area of Hadamard matrices and their applications has steadily and rapidly grown, especially during the last three decades. These matrices can be transformed to produce incomplete block designs, $t$-designs, Youden designs, orthogonal $F$-square designs, optimal saturated resolution III designs, optimal weighing designs, maximal sets of pairwise independent random variables with uniform measure, error correcting and detecting codes, Walsh functions, and other mathematical and statistical objects. In this paper we survey the existence of Hadamard matrices and many of their applications.read more
Citations
More filters
Using successive difference replication for estimating variances
TL;DR: Fay and Train this article presented a method called successive difference replication (SDR) that can be used to estimate the variance of an estimated total from a systematic random sample from an ordered list.
Journal ArticleDOI
Design and Evaluation of Sustained-Release Tablets of Lithium in a Fat Matrix and Its Bioavailability in Humans
Matías Llabrés,José B. Fariña +1 more
TL;DR: The results obtained show that the bioavailability of the formulation is 75% of the immediate-release formulation used as control and that the release rate, although close to the desired value, lasts only 7 or 8 h; these results agree with those given by numerical deconvolution using the mean urinary excretion curves.
Journal ArticleDOI
Least squares computations and the condition of the matrix
TL;DR: In the days of Von Neumann and Goldstine (1947), when matrix inversion was in vogue, the condition of the regression matrix in least squares problems held great relevance to both the sensitivity of its inverse to relatively small perturbations in its coefficients, and also to the number of decimal digit accuracy that could be obtained in the solution of the system of equations.
Posted Content
Painless Breakups -- Efficient Demixing of Low Rank Matrices
Thomas Strohmer,Ke Wei +1 more
TL;DR: In this paper, the authors presented two computationally efficient algorithms based on hard thresholding to solve the low rank demixing problem, which are guaranteed to converge to the correct solution at a linear rate.
Posted Content
Searching for partial Hadamard matrices
Víctor Álvarez,José Andrés Armario,M. D. Frau,Félix Gudiel,Maria Belen Guemes,Elena Barbadilla Martín,Amparo Osuna +6 more
TL;DR: In this paper, three algorithms for finding cliques of order m in a graph are described, where the key idea is characterizing the adjacency properties of vertices in a particular subgraph G_t of Ito's Hadamard Graph Delta (4t) [Ito85].