A different generalization is obtained by considering the equation for the scalar variance, , and reinterpreting as the squared Euclidean distance between the random variable and its mean, or, simply as the scalar product of the vector with itself. This results in which is the trace of the covariance matrix.
a dIffERenT GeNERAlizATioN Is obtAInED by considErinG tHe equATion for tHe sCaLaR variance, , anD reINterpreTiNG as the sqUaReD EuclideaN DistaNce BEtween the random varIaBle And iTs mEan, OR, simply As The scalAr PROdUcT Of thE veCToR with itsELf. tHis rEsults iN which is the tracE Of tHE covARianCe matRiX.