Juxtaposition means combine in the obvious way

In an expression, putting two things immediately next to each other usually means that they should be combined in some way. It's usually implicit that the combination operation should be clear from the context.

Examples

• Multiplication: \(ab = a \times b\).
• Function composition: \(fg(x) = f \circ g(x) = f(g(x))\).
• Function application: \(\sin x\).
• Group operation: when \(x,y \in G = (X,\star)\), \(xy = x \star y\).
• A linear transformation: \(\mathrm{A}\mathbf{v}\). (I've never seen \(\mathrm{A} \times \mathbf{v}\) or \(\mathrm{A} \cdot \mathbf{v}\) for matrix-vector product)

Exceptions

• Matrix indices written without a comma.