x×q×y

The expression x×q×y denotes the product of three objects x, q, and y under a binary operation indicated by the symbol ×. Its meaning depends on the mathematical context in which it appears; × is commonly used to denote multiplication, the cross product, or, in set theory, the Cartesian product.

In an algebraic setting, x, q, and y may be elements of a ring, group, or matrix algebra, with × representing the binary operation of that structure. If the operation is associative, the expression can be evaluated unambiguously as (x×q)×y or x×(q×y). If associativity does not hold, parentheses are essential to specify the order of multiplication.

In set theory, X × Q × Y is commonly used to denote the Cartesian product of sets X, Q, and Y, yielding the set of all ordered triples (x, q, y) with x∈X, q∈Q, and y∈Y. The cardinality of this product is |X|·|Q|·|Y|.

In linear algebra, × may denote matrix or scalar multiplication. The expression x × q × y is not standard notation; more typical forms are x^T Q y for vectors x,y and a matrix Q, or (x Q) y with explicit parentheses to indicate the intended order of operations.

Caveats and conventions: without explicit context or parentheses, the expression is ambiguous. Different mathematical structures enforce different rules for associativity and dimensional compatibility, so one should specify the operation and the domain to avoid misinterpretation.