Hilbert Matrix/Examples/3x3

Examples of Hilbert Matrices

The order $3$ Hilbert matrix is:

$H_3 = \begin {bmatrix}

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 {bmatrix}$

Determinant

The determinant of the order $3$ Hilbert matrix is given by:

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

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