**Defined in theory: Tensor-quantities****Source code: tensor-quantities.lisp**

**Documentation:**The class of quantities which are n-dimensional vectors (first order tensor-quantities). Each vector has an associated spatial dimension and an associated physical dimension. Each vector-quantity can be decomposed into scalar components for a given orthonormal basis of the proper dimension. The physical-dimension of a scalar component of the vector-quantity is equivalent to the physical-dimension of the vector-quantity.

**Subclass-Of:**Constant-quantity, Tensor-quantity

**Tensor-Order:**1

(<=> (Vector-Quantity ?V) (And (Constant-Quantity ?V) (Tensor-Quantity ?V) (= (Tensor-Order ?V) 1) (Forall (?B ?I) (=> (And (Orthonormal-Basis ?B) (= (Basis.Dimension ?B) (Spatial.Dimension ?V)) (Positive-Integer ?I) (=< ?I (Spatial.Dimension ?V))) (And (Defined (Vector-Component ?V ?I ?B)) (= (Quantity.Dimension (Vector-Component ?V ?I ?B)) (Quantity.Dimension ?V))))) (Forall (?U) (=> (And (Unit-Of-Measure ?U) (= (Quantity.Dimension ?U) (Quantity.Dimension ?V))) (Numeric-Tensor (Magnitude ?V ?U))))))