Function THE-VECTOR-QUANTITY

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

Slots on this function:

Documentation:

Constructor function for vector quantities (first order tensors). Requires a matrix and an orthnormal-basis as arguments. The constructed vector-quantity is equal to the sum of matrix elements multiplied by their corresponding basis vectors.

Arity: 3

Axioms:

(Nth-Domain The-Vector-Quantity 3 Vector-Quantity)

(Nth-Domain The-Vector-Quantity 2 Orthonormal-Basis)

(Nth-Domain The-Vector-Quantity 1 Row-Matrix)

(Nth-Domain The-Vector-Quantity 1 Matrix-Quantity)

(<=> (The-Vector-Quantity ?M ?B ?V)
     (And (Matrix-Quantity ?M)
          (Row-Matrix ?M)
          (Orthonormal-Basis ?B)
          (= (Quantity.Dimension ?V) (Quantity.Dimension ?M))
          (= (Column-Dimension ?M) (Basis.Dimension ?B))
          (= (Spatial.Dimension ?V) (Column-Dimension ?M))
          (Vector-Quantity ?V)
          (= ?V
             (Summation (Lambda (?J)
                                (* (Value ?M 1 ?J) (Basis.Vec ?B ?J)))
                        1
                        (Spatial.Dimension ?V)))))

Notes:

• Example: (= (the-vector-quantity (matrix-of-columns (* 3 feet) (* 1 yard)) 2d-frame-n) (* (the-vector-quantity (matrix-of-columns 3 3) 2d-frame-n) feet))