Function MATRIX-LESS-ROW-AND-COLUMN

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

Slots on this function:

Documentation:

Function that returns the matrix with a row and a column deleted

Instance-Of: Function

Arity: 4

Equivalence Axioms:

(<=> (Matrix-Less-Row-And-Column ?A ?I ?J)
     (And (Matrix ?A)
          (Defined (Row ?A ?I))
          (Defined (Column ?A ?J))
          (Matrix ?B)
          (= (Row-Dimension ?B) (- (Row-Dimension ?A) 1))
          (= (Column-Dimension ?B) (- (Column-Dimension ?A) 1))
          (= ?B (Matrix-Less-Row (Matrix-Less-Column ?A ?J) ?I))))

Axioms:

(Nth-Domain Matrix-Less-Row-And-Column 4 Matrix)

(Nth-Domain Matrix-Less-Row-And-Column 1 Matrix)

Other Related Axioms:

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

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B)
    (= ?B (Matrix-Less-Row (Matrix-Less-Column ?A ?J) ?I)))

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B)
    (= (Column-Dimension ?B) (- (Column-Dimension ?A) 1)))

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B)
    (= (Row-Dimension ?B) (- (Row-Dimension ?A) 1)))

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B) (Matrix ?B))

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B)
    (Defined (Column ?A ?J)))

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B)
    (Defined (Row ?A ?I)))

(=> (= (Matrix-Less-Row-And-Column ?A ?I ?J) ?B) (Matrix ?A))