28.2 Positive Definite Matrix

Types: N/A
Examples: 28.3 How to Identify if 2x2 Matrix is Positive Definite
Constructions: N/A
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Positive Definite Matrix

We say that an $n \times n$ matrix $K$ is positive definite iff it satisfies the two conditions:

Symmetry condition: $K = K^{T}$
Positivity condition: If $\vec{x} \neq \vec{0}$ , then ${\vec{x}}^{T} K \vec{x} > 0$

For short hand, we sometimes write $K > 0$ to imply that $K$ is a symmetric, positive definite matrix.

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