Algebra over Field/Examples/Vectors in 3-Space with Vector Product

Examples of Algebras over Fields

Let $V$ be the vector space formed of the set of all vectors in space.

Then $\struct {V, \times}$ forms an algebra over the field of vectors in space where $\times$ is the vector cross product.

Proof

This theorem requires a proof. In particular: I'm not immediately sure which is actually the underlying field in this case, I need to review my material. Unless someone else makes sense of this. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): algebra: 2.