Matrix Algebra

By S. Jeff

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Citations in the corpus

Stochastic Primal-Dual Q-Learning (2018, neutral): “Since P θ is a row stochastic matrix, we can enumerate the eigenvalues as Gentle (2007, pp. 306)).”
A matrix handbook for statisticians (2007, methodology): “2.1 2.2 2.3 Vector Spaces 2.1.1 Definitions 2.1.2 Quadratic Subspaces 2.1.3 2.1.4 Span and Basis 2.1.5 Isomorphism Inner Products 2.2.1 Definition and Properties 2.2.2 Functionals 2.2.3 Orthogonality 2.2.4 Column and Null Spaces Projections Sums and Intersections of Subspaces xvi 7 7 7 9 10 11 12 13”
Efficient Posterior Simulation for Cointegrated Models with Priors on the Cointegration Space (2009, background): “The matrix square root is de…ned, e.g., in Abadir and Magnus (2005), pages 220-221.”
New HEAVY Models for Fat-Tailed Realized Covariances and Returns (2017, background): “See for instance Abadir and Magnus (2005) for these and other useful results.”
High wage workers and low wage firms: negative assortative matching or limited mobility bias? (2008, methodology): “for A and B of the same order (Abadir and Magnus (2005), page 325).”
A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations (2011, methodology): “An introductory but detailed treatment of matrix calculus in econometrics is presented by Abadir and Magnus (2005). To apply the GAS framework to the multivariate Student’s t density (1) with Dt = I in (2), we require the score vector and the information matrix in (6) and (7) with respect to qt = ve”
Maximum likelihood estimation of a spatial autoregressive Tobit model (2015, background): “From Exercise 12.39 in Abadir and Magnus (2005), for any symmetric matrix M and compatible vector x, x M x min eig(M )x x, where min eig(M ) is the minimum characteristic root of M .”
Author ' s personal copy Partial Least Squares ( PLS ) methods for neuroimaging : A tutorial and review (2011, unknown): “For convenience, Appendix A also lists our main notations and acronyms (see also Abdi and Williams, 2010c, for more details on matrices).”
Testing the Equality of Covariance Operators in Functional Samples (2011, methodology): “(7) For the properties of the vech operator we refer to Abadir & Magnus (2005).”
Learning Laplacian Matrix in Smooth Graph Signal Representations (2014, background): “(17) as: arg min vech(L) α vec(Y Y T )T Mdup vech(L) +β vech(L)T MTdup Mdup vech(L), s.t.”