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×F is not a term with a single universal meaning; in mathematical notation it most often denotes a cross product with a fixed vector F. When you have a fixed vector F in three-dimensional space, the map that sends a vector v to v × F is a linear operator on R^3. This operator can be represented by a skew-symmetric 3×3 matrix [F]×, defined so that [F]× v = F × v. Consequently, v × F = - [F]× v. An explicit form for [F]×, given F = (F1, F2, F3), is the matrix

[ [0, -F3, F2],

[F3, 0, -F1],

[-F2, F1, 0] ].

Thus ×F expresses the cross product with F either as a binary operation on vectors (v × F) or, equivalently, as the action of the skew-symmetric operator represented by [F]×.

In physics and engineering, the cross product with F commonly arises when F represents a force or a fixed vector field. For example, torque is given by r × F, the cross product of the position vector r with a force F. The notation ×F may appear in discussions of linear operators derived from cross products or in vector-calculus identities that involve taking a cross product with a fixed vector.

Limitations and context matter. The cross product is defined specifically in three-dimensional Euclidean space (and has a related, but different, interpretation in higher dimensions). Therefore, the meaning of ×F should be inferred from the surrounding mathematical or physical context.

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