Positive Definite Matrix has Cholesky Factorization

Theorem

Let $\mathbf A$ be a positive definite matrix.

Then there exists a Cholesky factorization of $\mathbf A$.

Proof

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Sources

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