p×q

p×q is a compact notation that can denote more than one operation, depending on the mathematical context. In elementary arithmetic, p and q are numbers and p×q denotes their product; in geometry, the product corresponds to the area of a rectangle with sides p and q. When p and q are primes, p×q is a semiprime with divisors 1, p, q, and pq; if p = q, the product is p^2, with divisors 1, p, p^2.

In vector mathematics, p×q commonly denotes the cross product of vectors p and q in three-dimensional space. The result is a vector orthogonal to both p and q, with magnitude |p||q|sinθ, where θ is the angle between them. The direction is given by the right-hand rule; the cross product is bilinear and anti-commutative: p×q = -q×p, and p×p = 0.

Other uses include the Cartesian product in set theory in some texts when lowercase letters are used; more often, the notation A×B denotes the Cartesian product of sets A and B, the set of all ordered pairs (a,b) with a ∈ A and b ∈ B. In algebraic contexts p×q can denote a product in a given algebra, but the exact definition depends on the structure being studied.