Question

The infinity norm condition number of the 8x8 Hilbert matrix A with entries aij = 1/(i j-1) is approximately 3 x 10^n for some integer n. Enter n as your answer:

a) n = 8
b) n = 5
c) n = 3
d) n = 2

Answer 1

The infinity norm condition number of the 8x8 Hilbert matrix A can be calculated by finding the maximum absolute row sum of A and then multiplying it by the maximum absolute row sum of the inverse of A.

Step-by-step explanation:

The infinity norm condition number of the 8x8 Hilbert matrix A can be calculated by finding the maximum absolute row sum of A and then multiplying it by the maximum absolute row sum of the inverse of A. In this case, the entries of the Hilbert matrix are given by aij = 1/(i j-1). To find the maximum absolute row sum, we sum the absolute values of the entries in each row and take the maximum of these sums. The condition number is then given by the product of the maximum absolute row sum of A and the maximum absolute row sum of the inverse of A. In this case, the condition number is approximately 3 x 10n for some integer n.