Function SIZE

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

Slots on this function:

Documentation:

Size is the number of row or column of a square matrix

Instance-Of: Function

Arity: 2

Domain: Square-matrix

Equivalence Axioms:

(<=> (Size ?M) (And (Square-Matrix ?M) (= ?N (Row-Dimension ?M))))

Other Related Axioms:

(=> (Size $X $Y) (Square-Matrix $X))

(=> (= (Size ?M) ?N) (= ?N (Row-Dimension ?M)))

(=> (= (Size ?M) ?N) (Square-Matrix ?M))

(=> (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) (< 1 (Size ?M)))