已知n维随机变量\(\vec{X}=(X_{1},X_{2},...,X_{n})\)的协方差矩阵为\(C = \begin{bmatrix}c_{11} & c_{12} & ... & c_{1n} \\c_{21} & c_{22} & ... & c_{2n} \\. & .& &.\\. & .& &.\\. & .& &.\\c_{n1} & c_{n2} &...&c_{nn}\end{bmatrix} \)，其中\(c_{ij} = E\big\{[X_{i}-E(X_{i})][X_{j}-E(X_{j})]\big\}\)。那么，如何将协方差矩阵写成向量形式呢？
设\(X_{i}\)的样本量为m，则\(C = \frac{1}{m}\begin{bmatrix} (X_{1}-E(X_{1}))^{T}(X_{1}-E(X_{1})) & ... & (X_{1}-E(X_{1}))^{T}(X_{n}-E(X_{n})) \\ (X_{2}-E(X_{2}))^{T}(X_{1}-E(X_{1})) & ... & (X_{2}-E(X_{2}))^{T}(X_{n}-E(X_{n})) \\. &. & .\\. &. & .\\. &. & .\\ (X_{n}-E(X_{n}))^{T}(X_{1}-E(X_{1})) & ... & (X_{n}-E(X_{n}))^{T}(X_{n}-E(X_{n})) \end{bmatrix} \)
原文：http://www.cnblogs.com/thinkers-dym/p/4492817.html