Lecture

Equivalence Classes: Decomposition and Quotient Set

Related lectures (32)

Explores equivalence relations, reflexivity, equivalence classes, and constructing new sets based on equivalent elements.

Equivalence Classes

Introduces equivalence classes for decomposing a set into subsets of equivalent elements, defining the quotient set X/~.

Equivalence Classes and Relations

Covers equivalence classes, relations, quotient sets, and functions properties.

Kähler Differentials

Covers the concept of Kähler differentials, exploring linearity, construction, and B-linearity in algebraic geometry.

Linear Algebra: Bases and Transformations

Covers bases, transformations, and matrix decompositions in linear algebra.

Norms and Valuations on Fields

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Quotient Spaces: Three Ways

Explores three ways to form quotient spaces using group actions and equivalence relations.

Construction of an Iterative Method

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

Construction of Solutions by Dirichlet-Laplace

Explores the construction of solutions by Dirichlet-Laplace in general domains.

Equivalence Relations and Construction of R

Covers the construction of R and equivalence relations in sequences and linear recurrences.

Ring Operations: Ideals and Classes

Covers the operations in rings, ideals, classes, and quotient rings.

Exploration Bias

Explores regularization, learning algorithms, and subgaussian assumptions in machine learning.

Quotient by a Relation

Covers the concept of quotient space by a relation and its applications.

Project Management in Civil Engineering: Key Phases and Considerations

Provides an overview of project management phases in civil engineering, focusing on SIA 103 standards and stakeholder roles.

Homotopy Equivalence in Chain Complexes

Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.

Orthogonality and Characters

Explores the concepts of orthogonality and characters in vector spaces.

Matrix Factorization: LU Decomposition

Explores LU decomposition for matrix factorization and solving linear systems.

Introduction to Precast

Introduces precast concrete structures and advanced design techniques, covering topics like prefabrication, building connections, and construction projects.

Parametric Prefabrication

Explores parametric prefabrication in architecture using digital tools for building design and construction.