
5.1.83 luinverse
Syntax:
luinverse ( matrix_expression )
Type:
 matrix
Syntax:
luinverse ( matrix_expression, matrix_expression, matrix_expression )
Type:
 matrix
Purpose:
 Computes the inverse of a matrix A, if A is invertible.
The matrix A must be given either directly, or by its LUdecomposition.
In the latter case, three matrices P, L, and U are expected, in this order,
which satisfy
 P * A = L * U,
 P is an (m x m) permutation matrix, i.e., its rows/columns form the
standard basis of K^m,
 L is an (m x m) matrix in lower triangular form with all diagonal
entries equal to 1, and
 U is an (m x m) matrix in upper row echelon form.
Then, the inverse of A exists if and only if U is invertible, and one has
,since P is selfinverse.
In the case of A being given directly, luinverse first computes its
LUdecomposition, and then proceeds as in the case when P, L, and U are
provided.
list L=luinverse(A); fills the list L with either one entry = 0
(signaling that A is not invertible), or with the two entries
.Thus, in either case the user may first check the condition
L[1]==1 to find out whether A is invertible.
Note:
 The method will give a warning for any nonquadratic matrix A.
Example:
 ring r=0,(x),dp;
matrix A[3][3]=1,2,3,1,1,1,2,2,1;
list L = luinverse(A);
if (L[1] == 1)
{
print(L[2]);
" next should be the (3 x 3)unit matrix:";
print(A*L[2]);
}
==> 1,4, 1,
==> 1, 5,2,
==> 0, 2, 1
==>  next should be the (3 x 3)unit matrix:
==> 1,0,0,
==> 0,1,0,
==> 0,0,1

See
ludecomp.
