Hilbert Matrix is Positive Definite

Theorem

Let $\mathbf A$ be a Hilbert matrix.

Then $\mathbf A$ is positive definite

Proof

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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