A×Bmn

A×Bmn is not a standard, universally defined mathematical symbol. In published work the expression can be used in different ways depending on the field, the authors’ conventions, and the surrounding notation. Broadly speaking, A×Bmn stands for a binary operation involving a quantity A and a two-index object B with indices m and n. The exact definition, its algebraic properties, and the interpretation of the indices are context-dependent and must be stated explicitly by the source.

Possible interpretations include:

- A cross product variant: In three-dimensional vector calculus, × usually denotes a cross product between vectors. If Bmn is a component of a tensor or a vector-valued quantity labeled by indices m and n, the operation might be defined componentwise or through a specific contraction with a Levi-Civita symbol. Such definitions are not universal and require explicit specification.

- A tensorial or index-based construction: In tensor algebra, the symbol could denote a contraction, a tensor product, or an antisymmetrized combination defined by the author. For example, a third- or higher-rank tensor C with components C_i mn could be defined from A and B using a chosen formula, but the exact form depends on the convention.

- A field- or problem-specific operator: In physics or applied mathematics, A×Bmn may represent an operator acting on B or a particular coupling between A and components of B that arises from a specific model or equation.

Guidelines for interpretation:

- Look for an explicit definition or formula in the source.

- Check the dimensional consistency and index conventions.

- Consider how the indices m and n are used (row/column labels, spatial coordinates, or tensor indices).

Related concepts include the cross product, tensor product, and index notation with contractions and antisymmetrization.