Matrix: JGD_GL7d/GL7d13
Description: Differentials of the Voronoi complex of perfect forms of rank 7 mod GL_7(Z)
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| Matrix properties | |
| number of rows | 47,271 |
| number of columns | 8,899 |
| nonzeros | 356,232 |
| structural full rank? | no |
| structural rank | 8,897 |
| # of blocks from dmperm | 4 |
| # strongly connected comp. | 51 |
| explicit zero entries | 0 |
| nonzero pattern symmetry | 0% |
| numeric value symmetry | 0% |
| type | integer |
| structure | rectangular |
| Cholesky candidate? | no |
| positive definite? | no |
| author | P. Elbaz-Vincent |
| editor | J.-G. Dumas |
| date | 2008 |
| kind | combinatorial problem |
| 2D/3D problem? | 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/GL7d13.sms
| Ordering statistics: | result |
| nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 311,455,722 |
| nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 33,885,664 |
| SVD-based statistics: | |
| norm(A) | 15.2321 |
| min(svd(A)) | 0 |
| cond(A) | Inf |
| rank(A) | 7,938 |
| sprank(A)-rank(A) | 959 |
| null space dimension | 961 |
| full numerical rank? | no |
| singular value gap | 1.544e+13 |
| singular values (MAT file): | click here |
| SVD method used: | s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero |
| status: | ok |
For a description of the statistics displayed above, click here.
Maintained by Tim Davis, last updated 12-Mar-2014.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.