ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Ringoid
▼ Semiring
▼ Ring
▼ Left ring action
▼ Module
▼ Linear combination
▼ Linear map
▼ Multilinear map
▼ Bilinear map
▼ Sesquilinear map
▼ Hermitian map
▼ Hermitian form
▼ Semi-inner product
▼ Inner product
▼ Inner product space
Definition D37
Orthogonal vector pair
Formulation 1
Let $I$ be an D1128: Inner product space such that
(i) $\langle \cdot, \cdot \rangle$ is the D34: Inner product on $I$
(ii) $x, y \in I$ are each a D1129: Vector in $I$
Then $(x, y)$ is an orthogonal vector pair in $I$ if and only if \begin{equation} \langle x, y \rangle = 0 \end{equation}