(1.1 hours to learn)
A subspace is a subset of a vector space which is itself a vector space. Examples include spans of sets of vectors and solution sets to linear equations of the form Ax = 0.
This concept has the prerequisites:
- vectors (Subspaces are sets of vectors.)
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Khan Academy: Linear Algebra
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 1.3, "Subspaces of R^n," pages 16-22
- dot product
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 3.1, "Spaces of vectors," subsection "Subspaces," pages 121-123
Supplemental resources (the following are optional, but you may find them useful)
→ A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
Location: Section "Subspaces," pages 334-346
- vector spaces
- Gaussian elimination
- complex vectors and matrices
→ Linear Algebra Done Right
A textbook for a second course in linear algebra, with mathematical generalizations of the basic concepts.
Location: Chapter 1, "Vector spaces," section "Subspaces," pages 13-14
- Subspaces are used to define the rank of a matrix , an important concept in solving linear systems.
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