(1.3 hours to learn)
An orthonormal basis is a basis such that each vector has unit length and each pair of vectors is orthogonal. An orthonormal basis for the full space can be represented as an orthogonal matrix. Such matrices have nice algebraic properties and are useful for representing projections and least squares solutions.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Khan Academy: Linear Algebra
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 4.4, "Orthogonal bases and Gram-Schmidt," pages 234-238
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 5.5.2, "Orthogonal bases," pages 232-238
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