An introduction to optimization on smooth manifolds
2.5 Principal component analysis 19 2.6 Synchronization of rotations 22 2.7 Low-rank matrix completion 23 2.8 Gaussian mixture models 24 2.9 Smooth semidefinite programs 25 3 Embedded geometry: first order 27 3.1 Euclidean space 30 3.2 Embedded submanifolds of Euclidean space 33 3.3 Smooth maps on embedded submanifolds 40 3.4 The differential ...
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An introduction to optimization on smooth manifolds - EPFL
sma.epfl.chM† Moore–Penrose pseudoinverse of matrix M I d Identity matrix of size d I Subset of R (often open with 0 ∈I) or identity matrix Id Identity operator |a| Modulus of a∈C (absolute value if a∈R) |A| Cardinality of a set A E,E′,F Linear spaces, often with a Euclidean structure M,M′,M,N Smooth manifolds, often with a Riemannian structure
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