Vector Spaces and Subspaces

Linear independence, span, basis, and dimension

This module introduces the abstract structure that unifies all of linear algebra: vector spaces. You'll learn what it means for vectors to be linearly independent, what 'span' really means, and why choosing the right basis simplifies everything. These concepts are the vocabulary you need to understand PCA, SVD, and embedding spaces. Mini-lab: Find a basis for the column space of a matrix and verify that non-basis vectors can be written as linear combinations.

Estimated time: 60 minutes

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