# Function TENSOR-TO-MATRIX

## 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)