Definition:Symmetric Mapping (Linear Algebra)

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This page is about Symmetric Mapping in the context of Linear Algebra. For other uses, see Symmetry.


Let $\R$ be the field of real numbers.

Let $\F$ be a subfield of $\R$.

Let $V$ be a vector space over $\F$

Let $\innerprod \cdot \cdot: V \times V \to \mathbb F$ be a mapping.

Then $\innerprod \cdot \cdot: V \times V \to \mathbb F$ is symmetric if and only if:

$\forall x, y \in V: \innerprod x y = \innerprod y x$

Also see

Linguistic Note

This property as a noun is referred to as symmetry.