Eroxl's NotesGraph
Orthonormal Basis

An orthonormal basis is any basis formed from an orthonormal set, meaning its constituting vectors are mutually orthogonal and are unit vectors. Typically when writing an orthonormal basis we indicate this by representing each of its constituting vectors with .

Orthonormal bases allow for a large range of calculations to be simplified:

Computing -coordinates is one key example. For a general orthonormal basis of a subspace , the coordinates of any vector are given by: