Hilbert Matrix/Examples/3x3/Determinant/Mistake

Source Work

1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.)

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.):

Hilbert matrix

Mistake

For $n = 3$,

$H_3 = \begin {pmatrix} 1 & \tfrac 1 2 & \tfrac 1 3 \\ \tfrac 1 2 & \tfrac 1 3 & \tfrac 1 4 \\ \tfrac 1 3 & \tfrac 1 4 & \tfrac 1 5 \\ \end {pmatrix}$

and $\map \det {H_3} = 1 / 12 \, 160$.

Correction

The actual value is:

$\map \det {H_3} = 1 / 2160$

See On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008): A005249

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hilbert matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hilbert matrix