Lecture
Vector Spaces: Dimension and Generators
Related lectures (29)
Vector Spaces: Bases and Dimension
Explains bases and dimension in vector spaces, covering generative and free families, isomorphism, and key theorems.
Visualizing Fourth Dimension
Explores visualizing the Fourth Dimension and introduces vector spaces, linear applications, and transformations.
Orthogonality and Characters
Explores the concepts of orthogonality and characters in vector spaces.
Linear Transformations: Isomorphism and Dimension
Covers isomorphism, dimension, bases, and rank in linear transformations between vector spaces.
Linear Algebra in Dirac Notation
Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.
Normed Spaces
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Geometric Quantization: Representation Theory
Explores geometric quantization in representation theory, focusing on SO3(R) acting on R³ and homogenous polynomials.
Rank Theorem: Part 2MOOC: Algebra (part 1)
Delves into the Rank Theorem's implications for linear transformations and mappings.
Properties of Weak Derivatives
Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.
Basis of R^m
Introduces the concept of a basis of R^m and discusses homogeneous systems and vector spaces.