Function TRANSPOSE

• Defined in theory: Basic-matrix-algebra
• Source code: basic-matrix.lisp

Slots on this function:

Documentation:

Function that returns the matrix with lines and columns interchanged

the matrix (1 3) would be transformed into the matrix (1 2) (2 7) (3 7)

Instance-Of: Function

Arity: 2

Domain: Matrix

Range: Matrix

Equivalence Axioms:

(<=> (Transpose ?A)
     (And (Matrix ?A)
          (Matrix ?B)
          (= (Column-Dimension ?A) (Row-Dimension ?B))
          (= (Row-Dimension ?A) (Column-Dimension ?B))
          (Forall (?I ?J) (= (Value ?A ?I ?J) (Value ?B ?J ?I)))))

Other Related Axioms:

(=> (Transpose $X $Y) (Matrix $Y))

(=> (Transpose $X $Y) (Matrix $X))

(=> (= (Transpose ?A) ?B)
    (Forall (?I ?J) (= (Value ?A ?I ?J) (Value ?B ?J ?I))))

(=> (= (Transpose ?A) ?B)
    (= (Row-Dimension ?A) (Column-Dimension ?B)))

(=> (= (Transpose ?A) ?B)
    (= (Column-Dimension ?A) (Row-Dimension ?B)))

(=> (= (Transpose ?A) ?B) (Matrix ?B))

(=> (= (Transpose ?A) ?B) (Matrix ?A))

(Inherited-Facet-Value Same-Slot-Values
                       Orthogonal-Matrix
                       Transpose
                       Matrix-Inverse)

(<=> (Orthogonal-Matrix ?M)
     (And (Square-Matrix ?M)
          (Same-Values ?M Transpose Matrix-Inverse)))