orthogonal subspaces

(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.
Author: Gilbert Strang
Khan Academy: Linear Algebra


Supplemental resources (the following are optional, but you may find them useful)


See also

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