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

Example · Undergraduate

Terms

Term	This example	Why
bilinear form	✓	$(x, y) \mapsto x_1 y_1 - x_2 y_2$ is a bilinear form.
inner product	✗	$(x, y) \mapsto x_1 y_1 - x_2 y_2$ is not an inner product, because it is not positive definite: $(0, 1)$ paired with itself gives $-1$.

Distinctions using this example

• Dot product vs. inner product vs. bilinear form

All examples · All distinctions · All definitions