Inequalities: A Journey into Linear Analysis

By D. J. H. Garling. 2007

254 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9b99dc03bec8c1fe6a7a08fceb245611aae3389c

How researchers see this paper

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

In Applied Mathematics

Citations in the corpus

Connections with Robust PCA and the Role of Emergent Sparsity in Variational Autoencoder Models (2018, background): “The first inequality stems from Hadamard’s inequality (Garling, 2007) applied to 1 λ (W ∗∗)>W ∗∗ + I = M>M (29) for some square matrix M of appropriate dimension.”
Beyond traditional Curvature-Dimension I: new model spaces for isoperimetric and concentration inequalities in negative dimension (2014, methodology): “…interpretation when r = ∞ : Note that our normalization may diﬀer by some numerical constants from other variants used in the literature (our convention coincides with that of [23], which ensures that (cid:18) 1 A (cid:18) L α,r ( μ ) = μ ( A ) 1 /α for all r > 0, but diﬀers from that of [24]).”
Invariant Risk Minimization Games (2020, methodology): “t. In particular, since ( ) is dierentiable (Assumption 2), this means that the length of any partial derivative vector k( x) x i k for any coordinate i2[n]. Now, we apply the Hadamard inequality [42] for the determinant of the square matrix J(( x)): det(J(( x))) Q i2[n] k( x) x i k n. Therefore, Z”
Hidden Talents of the Variational Autoencoder. (2017, background): “Additionally, by Hadamard’s inequality [19] we have log ∣∣∣UΛ2U> + λI∣∣∣ = log ∣∣∣ 1 λWW + I∣∣∣+ d log λ (43)”
Tight Sample Complexity of Large-Margin Learning (2010, unknown): “A random variableX is sub-Gaussian with momentB (or B-sub-Gaussian) forB ≥ 0 if ∀t ∈ R, E[exp(tX)] ≤ exp(B2t2/2).”
On adaptive minimax density estimation on $$R^d$$Rd (2012, methodology): “Another lower bound on R in terms of ~L, ~r and θ can be established using the Littlewood interpolation inequality [see, e.g., (Garling 2007, Section 5.5)].”