# ISO: cross product

ISO norms specifies a standard symbol for cross product? I found in many books of mathematics the

\times


operator, while in physics it seems widely used the

 \wedge


(or \land or another similar symbol?) operator.

Which is the correct one to ISO norms?

-
As far as I know, both conventions are used in different communities. –  Corentin Oct 15 '12 at 19:59
@Corentin Of course. This was a "personal" statistics and it is meaningless for the question. ; ) (It was just not to put the two commands only.) –  R. M. Oct 15 '12 at 20:03

The standard ISO 80000-2, “Mathematical signs and symbols to be used in the natural sciences and technology”, specifies that the symbol for vector product (commonly known as cross product, too) is “×” MULTIPLICATION SIGN U+00D7. This corresponds to \times in LaTeX.

The “wedge” symbol “∧” denotes “logical and” by that standard and in common practice in formal logic. Using it for other purposes is thus nonstandard and potentially misleading.

-
Well, it's quite standard to use \wedge when talking about the wedge (exterior) product. –  Ipsen Oct 15 '12 at 20:58
The “wedge” symbol “∧” is used as the “logical and”, but it is also used by many authors as the "wedge or exterior product" of two vectors. –  Américo Tavares Oct 15 '12 at 21:00
\wedge is also used in Topology, to denote the quotient space $X\wedge Y=X\times Y / X\vee Y$, called the smash product of $X$ and $Y$. –  Sigur Oct 16 '12 at 0:41
@Sigur Mathematicians are not subject to that ISO regulation, and no regulation would be able to tame them. The \wedge symbol is used for very different operations, for example it's widely used as a connective in formal logic ("and") or to denote the infimum in lattices (e.g., Boolean algebras). The ISO standard is for what its title specifies: math symbols to be used in natural sciences and technology. –  egreg Oct 16 '12 at 6:52
You can use any symbol you want for any mathematical action you want, as long as you define it properly. In "tropical algebras" you say "multiplication is addition and addition is minimization". Btw, \wedge and \vee are used not only in logic, but in a whole theory of lattices, as sort-of generalization of and and or. And ISO standard cannot stop physicists neither, because they need new and new things that no standard can cover. –  tohecz Oct 16 '12 at 7:29
show 1 more comment

u × v means the cross product of vectors u and v.

u ∧ v means the wedge product of any multivectors u and v. In three dimensional Euclidean space the wedge product and the cross product of two vectors are each other's Hodge dual.

So, × (\times) is the cross product and ∧ (\wedge) is the wedge product.

-
I didn't know there were any difference... Why they are used as the same thing in R^3? Which is the correct one to use in physics? –  R. M. Oct 15 '12 at 20:38
@R.M. Well, I would ask this question in physics.SE. In the meantime I saw that in the German version of the List of mathematical symbols the two symbols are called cross product (Kreuzprodukt) –  Américo Tavares Oct 15 '12 at 20:48
Because they basically mean the same thing on tensors of dimension one (=vectors). Their difference is in higher dimension tensors. –  tohecz Oct 16 '12 at 7:23