• 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
  • Click here for a list of all matrix groups

  • Matrix: JGD_GL6/GL6_D_9
  • Description: Differentials of the Voronoi complex of perfect forms of rank 6 mod GL_6(Z),
  • download as a MATLAB mat-file, file size: 14 KB. Use SJget(601) or SJget('JGD_GL6/GL6_D_9') in MATLAB.
  • download in Matrix Market format, file size: 14 KB.
  • download in Rutherford/Boeing format, file size: 11 KB.


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


    dmperm of JGD_GL6/GL6_D_9

    scc of JGD_GL6/GL6_D_9

    Matrix properties (click for a legend)  
    number of rows340
    number of columns545
    structural full rank?no
    structural rank337
    numerical rank 220
    dimension of the numerical null space325
    numerical rank / min(size(A))0.64706
    Euclidean norm of A 10.789
    calculated singular value # 2202.3125
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 2219.9358e-015
    gap in the singular values at the numerical rank:
    singular value # 220 / singular value # 221
    calculated condition number9.7493e+033
    # of blocks from dmperm3
    # strongly connected comp.5
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorP. Elbaz-Vincent
    editorJ.-G. Dumas
    kindcombinatorial problem
    2D/3D problem?no


    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,                
    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_9.sms                                     

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU81,508 85,051
    nnz(R) for QR, upper bound nnz(U) for LU41,483 42,967

    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.