The Handbook of Matrices

By H. Luetkepohl. 1996

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Poisoning Attacks against Support Vector Machines (2012, methodology): “(4)–(5) with respect to each component u l (1 ≤ l ≤ d ), we obtain, for any i ∈ S , which can be rewritten as The ﬁrst matrix can be inverted using the Sherman-Morrison-Woodbury formula (L¨utkepohl, 1996): where υ = Q − 1 ss y s and ζ = y s Q − 1 ss y s .”
Security Evaluation of Support Vector Machines in Adversarial Environments (2014, methodology): “Solving these equations and computing an inverse matrix via the Sherman-MorrisonWoodbury formula [48] yields the following gradients:”
Support vector machines under adversarial label contamination (2015, methodology): “The first matrix can be inverted using matrix block inversion [42]: [ Qss zs zs 0 ]−1”
Facilitating the application of Support Vector Regression by using a universal Pearson VII function based kernel (2006, background): “More useful and also easier to verify are the following two mathematical properties [17,19], which hold when a matrix A is symmetric:”
A Multivariate Generalized Orthogonal Factor GARCH Model (2007, methodology): “Then ∂g(θ) ∂ vec(R1)′ = [Lr(Ir2 + Krr)(Ir ⊗ R′1) : 0] def= G, where ⊗ denotes the Kronecker product [cf. result 10.5.1(2a) in Lütkepohl 1996].”
Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups (2002, background): “On identifying the Kraus operators Sm with a matrix representation thereof Sm, a wellknown result regarding Kronecker matrix (or tensor) products [7, 8] implies col(ρ(t)) = S(t) col(ρ) ≡ M ∑”
Quasi-Newton Methods: A New Direction (2012, background): “…of the matrix product AXB can be re-written as Some important properties of Kronecker products are The identities in the left column directly follow from (2), the less straightforward identities on the right can be found in matrix algebra collections (e.g., L¨utkepohl, 1996; Minka, 2000a).”
Adaptive computation and machine learning (1998, background): “For a more detailed treatment of matrices the interested reader is referred to (Harville 1997; Lütkepohl 1996).”
The Conditional Autoregressive Wishart Model for Multivariate Stock Market Volatility (2010, unknown): “They obtain as Aj = Ln(Aj ⊗Aj)Dn, Bi = Ln(Bi ⊗Bi)Dn, (8) where Ln and Dn denote the elimination and duplication matrix, respectively, de ned so that vec(X) = Dnvech(X) and vech(X) = Lnvec(X) for any symmetric n × n matrix X (see Lütkepohl, 1996, p. 9-10).”
Statistical Tests and Estimators of the Rank of a Matrix and Their Applications in Econometric Modelling (2009, unknown): “(21), (22), and (23) follow from Lütkepohl (1996, 10.6(2) and 9.5.3(1)(ii)), (Lütkepohl, 1996, 10.5.1(7)) and Lütkepohl (1996, 10.4.1(1)(iii) and 9.5.3(1)(ii)), respectively19.”