Function COFACTOR

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

Slots on this function:

Documentation:

Function that returns (expt -1 (+ ?i ?j)) * determinant of the matrix less the row ?i and column ?j

Instance-Of: Function

Arity: 4

Equivalence Axioms:

(<=> (Cofactor ?M ?I ?J)
     (And (Square-Matrix ?M)
          (< 1 (Size ?M))
          (Defined (Value ?M ?I ?J))
          (= ?Cof
             (* (Expt -1 (+ ?I ?J))
                (Determinant (Matrix-Less-Row-And-Column ?M ?I ?J))))))

Axioms:

(Nth-Domain Cofactor 1 Square-Matrix)

Other Related Axioms:

(=> (And (Square-Matrix ?M))
    (= (Determinant ?M)
       (Cond ((= 1 (Size ?M)) (Value ?M 1 1))
             ((< 1 (Size ?M))
              (Summation (Lambda (?J)
                                 (* (Value ?M 1 ?J)
                                    (Cofactor ?M 1 ?J)))
                         1
                         (Size ?M))))))

(=> (= (Cofactor ?M ?I ?J) ?Cof)
    (= ?Cof
       (* (Expt -1 (+ ?I ?J))
          (Determinant (Matrix-Less-Row-And-Column ?M ?I ?J)))))

(=> (= (Cofactor ?M ?I ?J) ?Cof) (Defined (Value ?M ?I ?J)))

(=> (= (Cofactor ?M ?I ?J) ?Cof) (< 1 (Size ?M)))

(=> (= (Cofactor ?M ?I ?J) ?Cof) (Square-Matrix ?M))