Class DIAGONAL-MATRIX

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

Slots on this class:

Documentation:

A diagonal-matrix is a matrix with 0 apart from the diagonal

Instance-Of: Class

Subclass-Of: Matrix, Square-matrix

Equivalence Axioms:

(<=> (Diagonal-Matrix ?M)
     (And (Matrix ?M)
          (Square-Matrix ?M)
          (Forall (?I ?J)
                  (=> (And (Defined (Value ?M ?I ?J)) (/= ?I ?J))
                      (Zero-Element (Value ?M ?I ?J))))))

Axioms:

(Forall (?I ?J)
        (=> (And (Defined (Value ?M ?I ?J)) (/= ?I ?J))
            (Zero-Element (Value ?M ?I ?J))))

(Square-Matrix ?M)

(Matrix ?M)

Other Related Axioms:

(<=> (Diagonal-Matrix ?M)
     (And (Matrix ?M)
          (Square-Matrix ?M)
          (Forall (?I ?J)
                  (=> (And (Defined (Value ?M ?I ?J)) (/= ?I ?J))
                      (Zero-Element (Value ?M ?I ?J))))))