Positive Semidefinite Matrix in Machine Learning
What is Positive Semidefinite (PSD) Matrix Definition Matrix $A \in \mathbb{R}^{n\times n}$ is positive semi-definite (PSD), denoted $A \succeq 0$, is defined as: $A = A^{T}$ ($A$ is symmetric) $x^{T}Ax \geq 0$ for all $x \in \mathbb{R}$ So from the definition, we can infer some properties of PSD matrix. Properties If $A \succeq 0 $ then $A$ is invertible and $A^{-1} \succeq 0$. If $A \succeq 0 $ , then $\forall Q \in \mathbb{R}^{n\times n}$, we have $Q^{T}AQ \succeq 0$....