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• W3168607775 abstract "We introduce the manifold of restricted n×n positive semidefinite matrices of fixed rank p, denoted S(n,p)⁎. The manifold itself is an open and dense submanifold of S(n,p), the manifold of n×n positive semidefinite matrices of the same rank p, when both are viewed as manifolds in Rn×n. This density is the key fact that makes the consideration of S(n,p)⁎ statistically meaningful. We furnish S(n,p)⁎ with a convenient, and geodesically complete, Riemannian geometry, as well as a Lie group structure, that permits analytical closed forms for endpoint geodesics, parallel transports, Fréchet means, exponential and logarithmic maps. This task is done partly through utilizing a reduced Cholesky decomposition, whose algorithm is also provided. We produce a second algorithm from this framework to estimate principal eigenspaces and demonstrate its superior performance over other existing algorithms." @default.
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• W3168607775 date "2023-05-01" @default.
• W3168607775 modified "2023-10-14" @default.
• W3168607775 title "Restricted Riemannian geometry for positive semidefinite matrices" @default.
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• W3168607775 doi "https://doi.org/10.1016/j.laa.2023.01.026" @default.
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