Two vectors are considered orthogonal if \(\langle u,v \rangle = 0\), that is, their inner product is \(0\).
See also orthogonality test.
orthogonality and \(0\)
- \(0\) is orthogonal to every vector in \(v\) because \(\langle 0,v \rangle=0\) for every \(v\) because of the properties of inner product
- \(0\) is the only vector orthogonal to itself as, by inner product definiteness, \(\langle v,v \rangle=0\) implies \(v=0\).