(i) | $\langle \cdot, \cdot \rangle$ is the D34: Inner product on $I$ |

(ii) | $x, y \in I$ are each a D1129: Vector in $I$ |

**orthogonal vector pair**in $I$ if and only if \begin{equation} \langle x, y \rangle = 0 \end{equation}

▾ 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

▾ 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

Formulation 1

Let $I$ be an D1128: Inner product space such that

Then $(x, y)$ is an **orthogonal vector pair** in $I$ if and only if
\begin{equation}
\langle x, y \rangle
= 0
\end{equation}

(i) | $\langle \cdot, \cdot \rangle$ is the D34: Inner product on $I$ |

(ii) | $x, y \in I$ are each a D1129: Vector in $I$ |