CC: | angel [...] feht.dgtu.donetsk.ua |

Subject: | Strange Rank (order) of matrix |

Sorry,
rank (order) of matrix is not correctly defined.
For example.
#############
use Math::MatrixReal;
my $A = Math::MatrixReal->new_from_cols([[1,2,1,3,2],[4,9,3,12,10],
[2,5,1,6,6],[0,2,-2,0,4],[-3,1,-9,-8,7]]);
my $B = Math::MatrixReal->new_from_cols([[0,0,0,0,0]]);
my($An, $Bn) = $A->normalize($B);
my $LR_matrix = $An->decompose_LR();
my $rank = $LR_matrix->rank_LR();
print"rank = $rank\n";
#########
Program output:
rank = 4
But rank of the matrix $A should be 3 !!!
Accordingly not all fundamental decisions are by means of method:
($dimension,$x_vector,$base_matrix) = $LR_matrix->solve_LR($Bn);
Output:
$dimension => 1 (but should be 2 !)
$base_matrix => col_vector: 1, -0.5, 0.5, 0, 0
(but should be still, example: 4, -1, 0, 0.5, 0)
Can there is a decision of this problem?
Many thanks.
Yours faithfully,
Alessandro