The 3 × 3 Hilbert matrix is

The n × n Hilbert matrix is H_n = [h_jk], where h_jk = 1/(j + k - 1). (Similar matrices occur in curve fitting by least squares.) Compute the condition number κ(H_n) for the matrix norm corresponding to the l_∞ - (or l₁-) vector norm, for n = 2, 3, · · ·, 6 (or further if you wish). Try to find a formula that gives reasonable approximate values of these rapidly growing numbers.

Solve a few linear systems of your choice, involving an H_n.