Hadamard Matrices and Their Applications

By Sos S. Agaian. 1985

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In Pure Mathematics

Citations in the corpus

Federated Learning with Autotuned Communication-Efficient Secure Aggregation (2019, background): “Furthermore, the same MSE is achieved when the random rotation is replaced with a structured random orthogonal matrix R = HD, where H is a Walsh-Hadamard matrix [3] and D is a random diagonal matrix with i.”
cpSGD: Communication-efficient and differentially-private distributed SGD (2018, background): “5) and H is a Walsh-Hadamard matrix [18].”
Distributed Mean Estimation with Limited Communication (2016, neutral): “H is a Walsh-Hadamard matrix [14].”
Fix your classifier: the marginal value of training the last weight layer (2018, methodology): “We further suggest the use of a Hadamard matrix (Hedayat et al., 1978) as the ﬁnal classiﬁcation transform.”
A matrix handbook for statisticians (2007, background): “Quadratic subspaces arise in certain inferential problems such as the estimation of variance components (Rao and Rao [1998: chapter 131). They also arise in testing multivariate linear hypotheses when the variance-covariance matrix has a certain structure or pattern (Rogers and Young [1978: 2041 and”
Geometry of Quantum States: Index (2007, background): “Real Hadamard matrices have many uses, and discrete mathematicians have spent much effort constructing them [448].”
Statistical Query Algorithms for Mean Vector Estimation and Stochastic Convex Optimization (2015, unknown): “3 (We refer the reader to Hedayat and Wallis [50] for more information on Hadamard matrices.)”
Construction, classification and parametrization of complex Hadamard matrices (2011, methodology): “For further applications we refer the reader to the manuals [1] and [67].”
A Concise Guide to Complex Hadamard Matrices (2005, background): “This wide class of matrices includes in particular these with orthogonal rows and columns.”
Hadamard Matrices of Order 32 (2013, unknown): “For surveys on Hadamard matrices, we refer the reader to [2, 7, 21].”
QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks (2024, background): “While the Hadamard conjecture states that ∃ H k ∀ k, 4 | k , finding such Hadamard matrices is still an open problem (Hedayat & Wallis, 1978).”
Deep Representation Learning with Target Coding (2015, methodology): “A Hadamard code can be generated from the Hadamard matrix (Hadamard 1893; Hedayat and Wallis 1978).”
QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY (2011, background): “• If r = 1 and the quantum design is real, then the matrices √ bÊ−1 i Êj are Hadamard matrices (see [2] and [75]).”