## JGD_Trefethen/Trefethen_300

Diagonal matrices with primes, Nick Trefethen, Oxford Univ.
Name Trefethen_300 JGD_Trefethen 2208 300 300 4,678 4,678 Combinatorial Problem Yes 2008 N. Trefethen J.-G. Dumas
Structural Rank 300 true 1 1 0 100% 100% yes yes integer
SVD Statistics
Matrix Norm 1.987272e+03
Minimum Singular Value 1.121046e+00
Condition Number 1.772695e+03
Rank 300
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
Download ```Diagonal matrices with primes, Nick Trefethen, Oxford Univ. From Jean-Guillaume Dumas' Sparse Integer Matrix Collection, http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html 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)? http://www.siam.org/news/news.php?id=388 Filename in JGD collection: Trefethen/trefethen_300.sms```