(1.6 hours to learn)
Two subspaces X and Y are orthogonal if any vector in X is orthogonal to any vector in Y. Canonical examples include the row space and nullspace, and the column space and left nullspace. Orthogonality is used to analyze projections and least squares approximation.
This concept has the prerequisites:
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
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 4.1, "Orthogonality of the four subspaces," pages 195-200
Supplemental resources (the following are optional, but you may find them useful)
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 4.4, "The four fundamental subspaces," pages 171-183
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