Riemannian metrics on positive definite matrices related to means
نویسندگان
چکیده
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....
متن کاملRiemannian metrics on positive de nite matrices related to means
The Riemannian metric on the manifold of positive de nite matrices is de ned by a kernel function in the form K D(H;K) = P i;j ( i; j) 1TrPiHPjK when P i iPi 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! G(D) is ...
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→ ...
متن کاملO ct 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→ ...
متن کاملRiemannian metrics on positive de nite matrices related to means Fumio Hiai 1 and D
The Riemannian metric on the manifold of positive de nite matrices is de ned by a kernel function in the formK D(H;K) = P i;j ( i; j) TrPiHPjK when P i iPi 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! G(D) is a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2009
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.01.025