Positive Definite Matrices

2019

Citations in the corpus

• On the Bures–Wasserstein distance between positive definite matrices (2017, unknown): “See [7] [8] [9] [10] [19] [23] [24] [25] [26].”
• Riemannian Approaches in Brain-Computer Interfaces: A Review (2017, unknown): “) and the exponential metric increasing (EMI) property shown in [25], [58] illustrates the”
• Transfer Learning: A Riemannian Geometry Framework With Applications to Brain–Computer Interfaces (2018, background): “Covariance matrices do not belong to an Euclidean space, instead they belong to the smooth Riemannian manifold of Symmetric Positive Definite (SPD) matrices [5].”
• More accurate numerical radius inequalities (I) (2019, background): “It is well known that a convex function in the usual sense is not necessarily operator convex, and it is also known that the function f(t) = t, r > 0 defined on [0,∞) is operator convex if and only if r ∈ [1, 2].”
• Riemannian geometry for EEG-based brain-computer interfaces; a primer and a review (2017, unknown): “A positive matrix has a long list of important algebraic and analytic properties, which can be found in the monograph of Bhatia [69].”
• A review of classification algorithms for EEG-based brain–computer interfaces: a 10 year update (2018, methodology): “Amongst the most common matrix manifolds used for BCI applications, we encountered the manifold of Hermitian or symmetric positive definite (SPD) matrices [19] when dealing with covariance matrices estimated from EEG trials, and the Stiefel and Grassmann manifolds [62] when dealing with subspaces or”
• Positivity of $2\times 2$ block matrices of operators (2019, methodology): “We adopt some notation, facts and techniques from some books, say [9, 41, 43].”
• On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation (2016, result): “We refer to [3] for the following standard results.”