Comparing Tangent Vectors: Three Reasons Why

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Transporters: a proxy for parallel transport

Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.

Connections: Axiomatic Definition

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Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Momentum methods and nonlinear CG

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Manopt: Optimization Toolbox for Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.