orthonormal basis

Orthonormal basis

An orthonormal basis is an orthonormal set of vectors that span the space – exactly $n$ vectors in an $n$-dimensional space.

The identity matrix is the matrix representation of an orthonormal basis in the standard coordinate system.

For a matrix $V$, whose columns are the vectors of an arbitrary orthonormal basis, $V^{T}V=I$.

Note: "orthogonal/orthonormal matrix" is simply a unitary matrix in the context of real numbers (so refer to that note for more insights).

Also: By definition ($Q{Q}^T=I$) any orthogonal matrix is also orthonormal.