Hilbert Matrix/Examples/3x3
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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