• SJSU Singular Matrix Database
  • Matrix group: JGD_GL7d
  • Click here for a description of the JGD_GL7d group.
  • Click here for a list of all matrices
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  • Matrix: JGD_GL7d/GL7d25
  • Description: Differentials of the Voronoi complex of perfect forms of rank 7 mod GL_7(Z)
  • download as a MATLAB mat-file, file size: 256 KB. Use SJget(678) or SJget('JGD_GL7d/GL7d25') in MATLAB.
  • download in Matrix Market format, file size: 322 KB.
  • download in Rutherford/Boeing format, file size: 238 KB.

    JGD_GL7d/GL7d25

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    JGD_GL7d/GL7d25

    dmperm of JGD_GL7d/GL7d25

    scc of JGD_GL7d/GL7d25

    Matrix properties (click for a legend)  
    number of rows2,798
    number of columns21,074
    structural full rank?yes
    structural rank2,798
    numerical rank 2,525
    dimension of the numerical null space18,549
    numerical rank / min(size(A))0.90243
    Euclidean norm of A 215.52
    calculated singular value # 25253.7113
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    5.9896e-010
    calculated singular value # 25269.0353e-014
    gap in the singular values at the numerical rank:
    singular value # 2525 / singular value # 2526
    4.1076e+013
    calculated condition number2.3632e+018
    condest-2
    nonzeros81,671
    # of blocks from dmperm2
    # strongly connected comp.62
    entries not in dmperm blocks7
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorP. Elbaz-Vincent
    editorJ.-G. Dumas
    date2008
    kindcombinatorial problem
    2D/3D problem?no
    SJid678
    UFid1,998

    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/GL7d25.sms                                  
    

    Ordering statistics:AMD METIS DMPERM+
    nnz(V) for QR, upper bound nnz(L) for LU31,718,443 25,255,702 32,823,270
    nnz(R) for QR, upper bound nnz(U) for LU2,263,947 2,034,411 2,313,029

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.