Class MATRIX-QUANTITY

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

Slots on this class:

Documentation:

Class of matrices whose elements are quantities

Instance-Of: Class

Subclass-Of: Matrix, Physical-quantity

Superclass-Of: Numeric-matrix

Equivalence Axioms:

(<=> (Matrix-Quantity ?M)
     (And (Matrix ?M)
          (Physical-Quantity ?M)
          (Forall (?I ?J)
                  (=> (Defined (Value ?M ?I ?J))
                      (= (Quantity.Dimension ?M)
                         (Quantity.Dimension (Value ?M ?I ?J)))))))

Axioms:

(Forall (?I ?J)
        (=> (Defined (Value ?M ?I ?J))
            (= (Quantity.Dimension ?M)
               (Quantity.Dimension (Value ?M ?I ?J)))))

(Physical-Quantity ?M)

(Matrix ?M)

Other Related Axioms:

(<=> (Matrix-Quantity ?M)
     (And (Matrix ?M)
          (Physical-Quantity ?M)
          (Forall (?I ?J)
                  (=> (Defined (Value ?M ?I ?J))
                      (= (Quantity.Dimension ?M)
                         (Quantity.Dimension (Value ?M ?I ?J)))))))

(<=> (Numeric-Matrix ?M)
     (And (Matrix-Quantity ?M) (Dimensionless-Quantity ?M)))

(Nth-Domain Tensor-To-Matrix 3 Matrix-Quantity)

(=> (= (Tensor-To-Matrix ?T ?Basis) ?M) (Matrix-Quantity ?M))

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

(=> (= (The-Vector-Quantity ?M ?B) ?V) (Matrix-Quantity ?M))

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

(=> (= (The-Dyad ?M ?B) ?T) (Matrix-Quantity ?M))