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Comparing Tangent Vectors: Parallel Transport
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Related lectures (32)
Smooth Manifolds: Setup
MOOC: Introduction to optimization on smooth manifolds: first order methods
Introduces smooth manifolds, emphasizing the importance of submanifolds of linear spaces.
Connections: motivation and definition
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Explores the definition of connections for smooth vector fields on manifolds.
Riemannian connections
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Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Covariant derivatives along curves
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Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.
Manopt: Optimization Toolbox for Manifolds
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Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.
General Manifolds and Topology
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Covers manifolds, topology, smooth maps, and tangent vectors in detail.
Gradients on Riemannian submanifolds, local frames
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Discusses gradients on Riemannian submanifolds and the construction of local frames.
Hessians, Symmetry and Examples: Sphere, Stiefel
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Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.
Manopt: Optimization on Manifolds
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Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.
All things Riemannian: metrics, (sub)manifolds and gradients
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Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.
Differentiability of Functions of Several Variables
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Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.
Optimization on Manifolds
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Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.
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