Orthonormal basis example

1. What is an orthonormal basis?
2. How do you determine if a set is an orthonormal basis?

What is an orthonormal basis?

An orthonormal set must be linearly independent, and so it is a vector basis for the space it spans. Such a basis is called an orthonormal basis. The simplest example of an orthonormal basis is the standard basis for Euclidean space . The vector is the vector with all 0s except for a 1 in the th coordinate.

How do you determine if a set is an orthonormal basis?

A set of vectors S is orthonormal if every vector in S has magnitude 1 and the set of vectors are mutually orthogonal.