Definition:Positive Definite Matrix/Definition 2
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Definition
Let $\mathbf A$ be a symmetric square matrix of order $n$.
$\mathbf A$ is positive definite if and only if:
- all the eigenvalues of $\mathbf A$ are strictly positive.
Also known as
Some sources hyphenate positive definite: positive-definite.
Some sources refer to a positive definite matrix as symmetric positive definite, but under our definition the symmetric part of the definition is redundant.
Also see
- Results about positive definite matrices can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): positive definite
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): positive definite