Function MATRIX-INVERSE

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

Slots on this function:

Documentation:

Function that returns the inversion of a matrix

Instance-Of: Function

Arity: 2

Domain: Invertible-matrix

Range: Invertible-matrix

Equivalence Axioms:

(<=> (Matrix-Inverse ?M)
     (And (Invertible-Matrix ?M)
          (Invertible-Matrix ?M-1)
          (Identity-Matrix (* ?M ?M-1))
          (Identity-Matrix (* ?M-1 ?M))))

Other Related Axioms:

(=> (Matrix-Inverse $X $Y) (Invertible-Matrix $Y))

(=> (Matrix-Inverse $X $Y) (Invertible-Matrix $X))

(=> (= (Matrix-Inverse ?M) ?M-1) (Identity-Matrix (* ?M-1 ?M)))

(=> (= (Matrix-Inverse ?M) ?M-1) (Identity-Matrix (* ?M ?M-1)))

(=> (= (Matrix-Inverse ?M) ?M-1) (Invertible-Matrix ?M-1))

(=> (= (Matrix-Inverse ?M) ?M-1) (Invertible-Matrix ?M))

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

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