information:extraction, information:filtering, information:classification, structural:expansion, quality:corruption
Matrix notation for the variance of a linear combination

Define X {\displaystyle X} as a column vector of n {\displaystyle n} random variables X 1, …, X n {\displaystyle X_{1},\ldots,X_{n}}, and c {\displaystyle c} as a column vector of n {\displaystyle n} scalars c 1, …, c n {\displaystyle c_{1},\ldots,c_{n}}. Therefore, c T X {\displaystyle c^{\mathsf {T}}X} is a linear combination of these random variables, where c T {\displaystyle c^{\mathsf {T}}} denotes the transpose of c {\displaystyle c}. Also let Σ {\displaystyle \Sigma } be the covariance matrix of X {\displaystyle X}. The variance of c T X {\displaystyle c^{\mathsf {T}}X} is then given by:

This implies that the variance of the mean can be written as (with a column vector of ones)