• SJSU Singular Matrix Database
  • Matrix group: JGD_GL6
  • Click here for a description of the JGD_GL6 group.
  • Click here for a list of all matrices
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  • Matrix: JGD_GL6/GL6_D_8
  • Description: Differentials of the Voronoi complex of perfect forms of rank 6 mod GL_6(Z),
  • download as a MATLAB mat-file, file size: 20 KB. Use SJget(612) or SJget('JGD_GL6/GL6_D_8') in MATLAB.
  • download in Matrix Market format, file size: 20 KB.
  • download in Rutherford/Boeing format, file size: 15 KB.

    JGD_GL6/GL6_D_8

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

    JGD_GL6/GL6_D_8

    dmperm of JGD_GL6/GL6_D_8

    scc of JGD_GL6/GL6_D_8

    Matrix properties (click for a legend)  
    number of rows544
    number of columns637
    structural full rank?no
    structural rank542
    numerical rank 324
    dimension of the numerical null space313
    numerical rank / min(size(A))0.59559
    Euclidean norm of A 15.298
    calculated singular value # 3242.6459
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.1315e-012
    calculated singular value # 3251.1218e-014
    gap in the singular values at the numerical rank:
    singular value # 324 / singular value # 325
    2.3587e+014
    calculated condition number1.4861e+031
    condest-2
    nonzeros6,153
    # of blocks from dmperm2
    # strongly connected comp.8
    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
    SJid612
    UFid1,980

    Notes:

    Differentials of the Voronoi complex of perfect forms of rank 6 mod GL_6(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   
                                                                                
    D_6  Smith Invariants = [ 1:156 ]                                           
    D_7  Smith Invariants = [ 1:307 2:3 60:2 ]                                  
    D_8  Smith Invariants = [ 1:320 2:1 6:2 12:1 ]                              
    D_9  Smith Invariants = [ 1:217 2:3 ]                                       
    D_10 Smith Invariants = [ 1:120 ]                                           
                                                                                
    Filename in JGD collection: GL6/D_8.sms                                     
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU125,445 124,363
    nnz(R) for QR, upper bound nnz(U) for LU110,076 116,300

    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.