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

Example · Undergraduate

Terms

Term	This example	Why
bilinear form	✓	$(x, y) \mapsto x_1 y_1 + x_2 y_2$ on $\reals^2$ is an inner product and a bilinear form, because it is the dot product.
inner product	✓	$(x, y) \mapsto x_1 y_1 + x_2 y_2$ is an inner product: the dot product on $\reals^2$.
dot product	✓	$(x, y) \mapsto x_1 y_1 + x_2 y_2$ is the dot product on $\reals^2$.

Distinctions using this example

• Dot product vs. inner product vs. bilinear form
• Norm vs. metric vs. inner product

All examples · All distinctions · All definitions