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}