Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
Name Trefethen_20000
Group JGD_Trefethen
Matrix ID 2213
Num Rows 20,000
Num Cols 20,000
Nonzeros 554,466
Pattern Entries 554,466
Kind Combinatorial Problem
Symmetric Yes
Date 2008
Author N. Trefethen
Editor J.-G. Dumas
Structural Rank 20,000
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate yes
Positive Definite yes
Type integer
SVD Statistics
Matrix Norm 2.247372e+05
Minimum Singular Value 1.120552e+00
Condition Number 2.005593e+05
Rank 20,000
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download Singular Values MATLAB
Download MATLAB Rutherford Boeing Matrix Market
Diagonal matrices with primes, Nick Trefethen, Oxford Univ.          
From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,         
Problem 7 of the Hundred-dollar, Hundred-digit Challenge Problems,   
SIAM News, vol 35, no. 1.                                            
7. Let A be the 20,000 x 20,000 matrix whose entries are zero        
everywhere except for the primes 2, 3, 5, 7, . . . , 224737 along the
main diagonal and the number 1 in all the positions A(i,j) with      
|i-j| = 1,2,4,8, . . . ,16384.  What is the (1,1) entry of inv(A)?   
Filename in JGD collection: Trefethen/trefethen_20000.sms