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@jemoka / Jemoka Knowledge Base / wiki/concepts/orthogonal.md
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--- title: "orthogonal" type: concept related: [Vector, Orthogonal, Inner Product] source: https://www.jemoka.com/posts/kbhorthogonal/ confidence: high status: active --- 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 \(v=0\).