Span — Topic Summaries
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Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
Linear combinations turn two (or more) vectors into a whole geometric “shape” of reachable results—and that shape is the span. In the 2D coordinate...
Abstract Linear Algebra 4 | Basis, Linear Independence, Generating Sets
The core takeaway is that “basis,” “linear independence,” and “dimension” from standard linear algebra extend cleanly to abstract vector...
Abstract Linear Algebra 4 | Basis, Linear Independence, Generating Sets [dark version]
A basis in abstract linear algebra is defined as the “sweet spot” between spanning and uniqueness: it generates a subspace while keeping linear...
Linear Algebra 23 | Linear Independence (Examples) [dark version]
Linear independence hinges on one test: a family of vectors is linearly independent exactly when the only way to combine them to get the zero vector...