Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices
2004 ◽
Vol 56
(4)
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pp. 776-793
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Keyword(s):
AbstractWe explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold Sym(n, ℝ)++ of positive definite matrices. An explicit calculation for the minimal distance function from the geodesic submanifold Sym(p, ℝ)++ × Sym(q, ℝ)++ block diagonally embedded in Sym(n, ℝ)++ is given in terms of metric and spectral geometric means, Cayley transform, and Schur complements of positive definite matrices when p ≤ 2 or q ≤ 2.
2011 ◽
Vol 435
(2)
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pp. 307-322
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2012 ◽
Vol 437
(9)
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pp. 2159-2172
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2015 ◽
Vol 64
(3)
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pp. 512-526
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1991 ◽
Vol 119
(3-4)
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pp. 233-240
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2007 ◽
Vol 29
(1)
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pp. 328-347
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2021 ◽
Vol 4
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pp. 100142