Vector Spaces: Dimension and Generators

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Related lectures (27)

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Vector Spaces: Bases and Dimension

Explains bases and dimension in vector spaces, covering generative and free families, isomorphism, and key theorems.

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Linear Algebra Basics

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Transformations: Matrices and Bases

Covers the method to calculate the images of vectors in a given base.

Visualizing the Fourth Dimension: A Mathematical Journey

Explores visualizing the Fourth Dimension through points, lines, circles, spheres, and punching through, covering vector space properties, dimensionality, bases, and theorems.

Linear Transformations: Isomorphism and Dimension

Covers isomorphism, dimension, bases, and rank in linear transformations between vector spaces.