Linear Applications and Simple Objects

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Related lectures (41)

Group Theory Fundamentals Log in to Mediaspace to watch this video

Introduces the basics of group theory, defining groups, categories, and groupoids.

Equivalences de Catégories et Adjonctions Log in to Mediaspace to watch this video

Explores category equivalences, adjunctions, and group actions in category theory.

Group Theory: Adjoint Functors and G-sets Log in to Mediaspace to watch this video

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Category Theory: Introduction Log in to Mediaspace to watch this video

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Group Actions and Functors Log in to Mediaspace to watch this video

Covers group quotient, group actions, and functors connecting sets and G-sets.

Limits and Colimits: Understanding Categories Log in to Mediaspace to watch this video

Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.

Introduction to Categories: Products and Coproducts Log in to Mediaspace to watch this video

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Active Learning Session Log in to Mediaspace to watch this video

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Adjunctions, Products, and Coproducts Log in to Mediaspace to watch this video

Discusses adjunctions, products, and coproducts in category theory.

Active Learning: Group Theory Log in to Mediaspace to watch this video

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Natural Transformations in Algebra Log in to Mediaspace to watch this video

Explores natural transformations in algebra, defining functors and isomorphisms.

Natural Transformations Log in to Mediaspace to watch this video

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Advanced Physics I: Introduction to Mechanics Log in to Mediaspace to watch this video

Introduces the basics of physics, including mechanics and making predictions based on observations and hypotheses.

Orthogonal Projection Theorems Log in to Mediaspace to watch this video

Covers the theorems related to orthogonal projection and orthonormal bases.

Seven-Eleven Japan Discussion: Supply Chain Excellence Log in to Mediaspace to watch this video

Explores Seven-Eleven Japan's operational excellence, focusing on data collection, distribution, inventory management, and value creation strategies.

Singular Value Decomposition Log in to Mediaspace to watch this video

Introduces Singular Value Decomposition (SVD) in linear algebra, covering matrix factorization and properties with practical examples.

Linear Transformations and Change of Bases Log in to Mediaspace to watch this video

Covers linear transformations, change of bases, and diagonalization of matrices.

Diagonalization of Symmetric Matrices Log in to Mediaspace to watch this video

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Speculative Query Execution: Bottlenecks and Dependencies Log in to Mediaspace to watch this video

Explores speculative query execution for complex queries, addressing bottlenecks, dependencies, and performance prediction.

Finite Element Method: Quadrangular Elements Log in to Mediaspace to watch this video

Explores basic functions and criteria in quadrangular finite elements using the finite element method.

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