Procrustes problems in Riemannian manifolds of positive definite matrices
نویسندگان
چکیده
منابع مشابه
Approximation Problems in the Riemannian Metric on Positive Definite Matrices
There has been considerable work on matrix approximation problems in the space of matrices with Euclidean and unitarily invariant norms. We initiate the study of approximation problems in the space P of all n×n positive definite matrices with the Riemannian metric δ2. Our main theorem reduces the approximation problem in P to an approximation problem in the space of Hermitian matrices and then ...
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The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function φ in the form K D(H,K) = ∑ i,j φ(λi, λj) −1TrPiHPjK when ∑ i λiPi is the spectral decomposition of the foot point D and the Hermitian matrices H,K are tangent vectors. For such kernel metrics the tangent space has an orthogonal decomposition. The pull-back of a kernel metric under a mapping D 7→ ...
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On the manifold of positive definite matrices, a Riemannian metric Kφ is associated with a positive kernel function φ on (0,∞) × (0,∞) by defining K D(H,K) = ∑ i,j φ(λi, λj) TrPiHPjK, where D is a foot point with the spectral decomposition D = ∑ i λiPi and H,K are Hermitian matrices (tangent vectors). We are concerned with the case φ(x, y) = M(x, y)θ where M(x, y) is a mean of scalars x, y > 0....
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2019
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.11.009