$(x, y) \mapsto 2 x_1 y_1 + x_2 y_2$ on $\reals^2$

Example · Undergraduate

Terms

Term	This example	Why
bilinear form	✓	$(x, y) \mapsto 2 x_1 y_1 + x_2 y_2$ is a bilinear form, because it is linear in $x$ and in $y$.
inner product	✓	$(x, y) \mapsto 2 x_1 y_1 + x_2 y_2$ is an inner product, because it is symmetric and positive definite.
dot product	✗	$(x, y) \mapsto 2 x_1 y_1 + x_2 y_2$ is not the dot product, because of the factor $2$.

Distinctions using this example

• Dot product vs. inner product vs. bilinear form

All examples · All distinctions · All definitions