orthonormal bases

(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)


MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
Author: Gilbert Strang


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


See also

  • Orthogonal matrices can be characterized in terms of eigenvalues having unit norm.
  • Orthogonal matrices are used in the spectral decomposition of a symmetric matrix.