Module 4: Vector Spaces
Explore the abstract structure of vector spaces: subspaces, span, linear independence, basis, and dimension.
Module Lessons
1
Vectors in R^n
Vector operations, geometric interpretation, and the dot product in R^n.
2
Subspaces, Span, and Linear Combinations
Define subspaces, express vectors as linear combinations, and compute the span of a set of vectors.
3
Linear Independence
Determine when a set of vectors is linearly independent or dependent, and understand the implications.
4
Basis and Dimension
Find bases for vector spaces, understand dimension, and relate basis to the rank of a matrix.