inv (Matrix)

Tries to invert a square matrix. If the matrix is invertible, the function returns

, where is the adjugate and is the determinant. If the inverse doesn't exist, the function returns , where c * M^T = <0> (zero vector).

Arguments

The square

to invert.

Return values

Resulting

, empty if it doesn't exist (see Matrix).
of the matrix, as a real number.
of the matrix, empty if it doesn't exist (see Vector).
is TRUE if the matrix can be inverted, FALSE otherwise.

Complexity

O(size^3)

Example

"sl/algebra" useFile checkedInv: [ inv [ drop "det:" print print LF print m:; m.rows [i m.rowRange [print "," print] each LF print] times ] [ v:; drop drop "v:" print LF print v.makeRange [print "," print] each ] if ] func; ((2.0 1.0 1.0) (-1.0 1.0 1.0) (0.0 2.0 -2.0)) makeMatrix checkedInv ((2.0 1.0 1.0) (-5.0 1.0 2.0) (-1.0 0.666666 1.0)) makeMatrix checkedInv
Output: