A notation for vectors and tensors

Extract

The vector notation commonly employed in elementary physics cannot be applied in its usual form to spaces of other than three dimensions. In plane dynamics, for instance, it cannot be used to represent the velocity (– ωx₂, ωx₁) at the point (x₁, x₂) due to a rotation ω about the origin, or the (scalar) moment about the origin of the force (F₁, F₂) acting at (x₁, x₂). In relativity physics the symbol ⋅ is often used to denote the scalar product of two vectors, it is true, and the tensor a_αb_β – a_βb_α is sometimes denoted by a × b, but there exists no body of rules for the manipulation of these symbols that enables one to dispense with the suffix notation as in the case of vectors in three-dimensional space.