Joker's Blog

设 $\pmb{x}$ 为 $n \times 1$ 维度的随机向量，记 $\pmb{A}$ 为 $n \times n$ 维度的矩阵，并设

$E[\pmb{x}] = \pmb{\mu}$

$Var[\pmb{x}] = \pmb{\Sigma}$

则由如下等式成立:

$E[\pmb{x}^T A \pmb{x}] = tr(\pmb{A}\pmb{\Sigma}) + \pmb{\mu}^T A \pmb{\mu}$

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随机向量的均值