{
    matrix_id: '1999',
    name: 'GL7d26',
    group: 'JGD_GL7d',
    description: 'Differentials of the Voronoi complex of perfect forms of rank 7 mod GL_7(Z)',
    author: 'P. Elbaz-Vincent',
    editor: 'J.-G. Dumas',
    date: '2008',
    kind: 'combinatorial problem',
    problem_2D_or_3D: '0',
    num_rows: '305',
    num_cols: '2798',
    nonzeros: '7412',
    num_explicit_zeros: '0',
    num_strongly_connected_components: '53',
    num_dmperm_blocks: '2',
    structural_full_rank: 'false',
    structural_rank: '303',
    pattern_symmetry: '0.000',
    numeric_symmetry: '0.000',
    rb_type: 'integer',
    structure: 'rectangular',
    cholesky_candidate: 'no',
    positive_definite: 'no',
    notes: 'Differentials of the Voronoi complex of perfect forms of rank 7 mod GL_7(Z)  
equivalences, (related to the cohomology of GL_7(Z) and the K-theory of Z).  
from Philippe Elbaz-Vincent, Institut Fourier, Grenoble, France.             
                                                                             
From Jean-Guillaume Dumas\' Sparse Integer Matrix Collection,                 
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html                    
                                                                             
http://www-fourier.ujf-grenoble.fr/-Informations-personnelles-.html?P=pev    
                                                                             
mtx rank        n       m       ker         rank/min(n,m)   homology         
10 1            60      1       59                                           
11 59           1019    60      960         0,98333         0                
12 960          8899    1019    7939        0,94210         1                
13 7938         47271   8899    39333       0,89201         1                
14 39332        171375  47271   132043      0,83205         0                
15 132043       460261  171375  328218      0,77049         0                
16 328218       955128  460261  626910      0,71311         0                
17 626910       1548650 955128  921740      0,65636         0*               
18 921740*      1955309 1548650 1033569*    0,60*           1/0*             
19 103356(8/9)* 1911130 1955309 87756(2/1)* 0,54*           0/1*             
20 877562       1437547 1911130 559985      0,61            0                
21 559985       822922  1437547 262937      0,68048         0                
22 262937       349443  822922  86506       0,75245         0                
23 86505        105054  349443  18549       0,82343         1                
24 18549        21074   105054  2525        0,88018         0                
25 2525         2798    21074   273         0,90243         0                
26 273          305     2798    32          0,89508         0                
                                                                             
file    size              elements  rank    SF                               
GL7d10  1 x 60            8         1       1 (1)                            
GL7d11  60 x 1019         1513      59      1 (59)                           
GL7d12  1019 x 8899       37519     960     1 (958), 2 (2)                   
GL7d13  8899 x 47271      356232    7938    1 (7937), 2 (1)                  
GL7d14  47271 x 171375    1831183   39332   1 (39300),2 (29),4 (3)           
GL7d15  171375 x 460261   6080381   132043  1 (131993), 2*??? (46), 6*??? (4)
GL7d16  955128 x 460261   14488881  328218                                   
GL7d17  1548650 x 955128  25978098                                           
GL7d18  1955309 x 1548650 35590540                                           
GL7d19  1911130 x 1955309 37322725                                           
GL7d20  1437547 x 1911130 29893084  877562                                   
GL7d21  822922 x 1437547  18174775  559985                                   
GL7d22  349443 x 822922   8251000   262937                                   
GL7d23  105054 x 349443   2695430   86505   1 (86488), 2*??? (12), 6*??? (5) 
GL7d24  21074 x 105054    593892    18549   1 (18544),2 (4),4 (1)            
GL7d25  21074 x 2798      81671     2525    1 (2507), 2 (18)                 
GL7d26  2798 x 305        7412      273     1 (258), 2 (7), 6 (7), 36 (1)    
                                                                             
Filename in JGD collection: GL7d/GL7d26.sms                                  
',
    norm: '1.307278e+03',
    min_singular_value: '2.172656e-16',
    condition_number: '6016956108131821568',
    svd_rank: '273',
    sprank_minus_rank: '30',
    null_space_dimension: '32',
    full_numerical_rank: 'no',
    svd_gap: '64002391464195.953125',
    image_files: 'GL7d26.png,GL7d26_dmperm.png,GL7d26_scc.png,GL7d26_svd.png,GL7d26_graph.gif,',
}
