The Matrix Cookbook

By Kaare Brandt Petersen, M. S. Pedersen. 2006

3,299 citations recorded by the source corpus.

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

Citations in the corpus

Meta-learning with differentiable closed-form solvers (2018, methodology): “To alleviate this, we rely on the Woodbury formula [27], obtaining: Λ(Z) = X (XX + λI) −1 Y.”
Robust Large Margin Deep Neural Networks (2016, background): “The gradient of gk (xi)gk (xi) with respect to Wl is then given as [45]”
Word Representations via Gaussian Embedding (2014, methodology): “Just as in the previous case, we can compute the gradients for this energy function in closed form: where Petersen, 2006).”
Off-policy evaluation for slate recommendation (2016, methodology): “Thus, Q is invertible To obtain Q − 1 , we use the following identity (see [18]): where M := A 11 − A 12 A − 1 22 A 21 is the Schur complement of A 22 .”
Residual Flows for Invertible Generative Modeling (2019, background): “(15) Note, that (13) follows from the chain rule of differentiation, for the derivative of the determinant in (14), see (Petersen and Pedersen, 2012, eq.”
Gaussian Processes for Data-Efficient Learning in Robotics and Control (2015, methodology): “ies that will become handy. After that we will detail derivative computations in the context of the momentmatching approximation. B.1 Identities Let us start with a set of basic derivative identities [2] that will prove useful in the following: @jK()j @ = jKjtr K 1 @K @ ; @jKj @K = jKj(K 1)>; @”
A Least-squares Approach to Direct Importance Estimation (2009, neutral): “The following inversion formula holds for block matrices (Petersen and Pedersen, 2007): ( M1 M2 M3 M4 )−1 = ( M−1 1 +M −1 1 M2M −1 0 M3M −1 1 −M−1 1 M2M 0 −M−1 0 M3M 1 M−1 0 ) , (14)”
Unsupervised Deep Slow Feature Analysis for Change Detection in Multi-Temporal Remote Sensing Images (2018, methodology): “According to the reference [43], and using the fact that Aφ and Bφ are both symmetric, we could then have:”
Deep Canonical Correlation Analysis (2013, background): “…that may account for deep networks’ success in other tasks—high model complexity, the ability to concisely represent a hierarchy of features for modeling real-world data distributions—could be particularly useful in a setting where the output space is significantly more complex than a single label.”
Revisiting Recursive Least Squares for Training Deep Neural Networks (2021, methodology): “We rewrite (25) and (26) as follows Let P Ls = ( A Ls ) − 1 and use the Kailath variant formula [42] for (25).”
Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs (2018, methodology): “The formula can be found, e.g., in Petersen et al. (2008).”
Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design (2008, background): “The computations are partly based on the result [16]: (cid:8) (cid:9) , where e n is a unity-vector with one at the n th element and zeros elsewhere.”
A Practical and Conceptual Framework for Learning in Control (2010, methodology): “We re-state results from the book by Petersen and Pedersen (2009) to compute derivatives of products, inverses, determinants,”
Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety (2011, background): “So all the expressions from the real-valued case given, for example, in [98], can be straightforwardly applied to the complex case.”