Matrix: JGD_G5/IG5-7

Description: Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.

 (bipartite graph drawing)

• Matrix group: JGD_G5
• download as a MATLAB mat-file, file size: 3 KB. Use UFget(1966) or UFget('JGD_G5/IG5-7') in MATLAB.

 Matrix properties number of rows 62 number of columns 150 nonzeros 549 structural full rank? yes structural rank 62 # of blocks from dmperm 1 # strongly connected comp. 76 explicit zero entries 0 nonzero pattern symmetry 0% numeric value symmetry 0% type integer structure rectangular Cholesky candidate? no positive definite? no

 author N. Thiery editor J.-G. Dumas date 2008 kind combinatorial problem 2D/3D problem? no

Notes:

```Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
Univ. Paris Sud.

From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,
http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html

http://www.lapcs.univ-lyon1.fr/~nthiery/LinearAlgebra/

Linear Algebra for combinatorics

Abstract:  Computations in algebraic combinatorics often boils down to
sparse linear algebra over some exact field. Such computations are
usually done in high level computer algebra systems like MuPAD or
Maple, which are reasonnably efficient when the ground field requires
symbolic computations. However, when the ground field is, say Q  or
Z/pZ, the use of external specialized libraries becomes necessary. This
document, geared toward developpers of such libraries, present a brief
overview of my needs, which seems to be fairly typical in the
community.

IG5-6: 30 x 77 : rang = 30  (Iteratif: 0.01 s, Gauss: 0.01 s)
IG5-7: 62 x 150 : rang = 62  (Iteratif: 0.02 s, Gauss: 0.01 s)
IG5-8: 156 x 292 : rang = 154  (Iteratif: 0.08 s, Gauss: 0.01 s)
IG5-9: 342 x 540 : rang = 308  (Iteratif: 0.46 s, Gauss: 0.02 s)
IG5-10: 652 x 976 : rang = 527  (Iteratif: 2.1 s, Gauss: 0.07 s)
IG5-11: 1227 x 1692 : rang = 902  (Iteratif: 7.5 s, Gauss: 0.22 s)
IG5-12: 2296 x 2875 : rang = 1578  (Iteratif: 26 s, Gauss: 0.93 s)
IG5-13: 3994 x 4731 : rang = 2532  (Iteratif: 80 s, Gauss: 3.35 s)
IG5-14: 6727 x 7621 : rang = 3906  (Iteratif: 244 s, Gauss: 10.06 s)
IG5-15: 11358 x 11987 : rang = 6146  (Iteratif: s, Gauss: 29.74 s)
IG5-16: 18485 x 18829 : rang = 9519  (Iteratif: s, Gauss: 621.97 s)
IG5-17: 27944 x 30131 : rang = 14060  (Iteratif: s, Gauss: 1973.8 s)

Filename in JGD collection: G5/IG5-7.txt2
```

 Ordering statistics: result nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 1,500 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 1,477

 SVD-based statistics: norm(A) 30.1432 min(svd(A)) 0.115596 cond(A) 260.764 rank(A) 62 sprank(A)-rank(A) 0 null space dimension 0 full numerical rank? yes

 singular values (MAT file): click here SVD method used: s = svd (full (A)) ; status: ok