منابع مشابه
Riemannian metrics on positive definite matrices related to means. II
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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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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متن کاملN ov 2 00 8 Riemannian metrics on positive definite matrices related to means
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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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1987
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1987.102190