Function TENSOR-TO-MATRIX

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

Slots on this function:

Documentation:

Function that maps a tensor to matrix for a particular basis. Tensor-to-Matrix is defined for first and second order tensors (vector-quantities & dyads). Tensor-to-Matrix maps a vector-quantity into a
row matrix of column-dimension equal to the spatial.dimension of the vector-quantity. Dyads are mapped into square matrices of row- and column-dimension equal to the spatial dimension of the dyad. The scalar components of the resulting matrices corresspond to dot (inner) products of the tensor with appropriate basis vectors.

Arity: 3

Axioms:

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

(Nth-Domain Tensor-To-Matrix 2 Orthonormal-Basis)

(Nth-Domain Tensor-To-Matrix 1 Tensor-Quantity)

(<=> (Tensor-To-Matrix ?T ?Basis ?M)
     (And (Tensor-Quantity ?T)
          (Orthonormal-Basis ?Basis)
          (=> (Member ?Q (Tensor-Order ?T)) (Member ?Q (Setof 1 2)))
          (Matrix-Quantity ?M)
          (=> (= (Tensor-Order ?T) 1)
              (= (Row-Dimension ?M) 1)
              (= (Column-Dimension ?M) (Spatial.Dimension ?T))
              (Forall (?I)
                      (= (Value ?M 1 ?I)
                         (Vector-Component ?T ?I ?Basis))))
          (=> (= (Tensor-Order ?T) 2)
              (Square-Matrix ?M)
              (= (Size ?M) (Spatial.Dimension ?T))
              (Forall (?I ?J)
                      (= (Value ?M ?I ?J)
                         (Dyad-Component ?T ?I ?J ?Basis))))))