Basic facts (Cont.)
Maximizing var(míx) subject to ||m||=1 is the same as Max mícov(X)m subject to ||m||=1
(here ||m|| denotes the length of the vector m)
Eigenvalue decomposition :
(B.2) M vi = _i vi, where
Basic linear algebra tells us that the first eigenvector will do :
Solution of max mí M m subject to ||m||=1 must satisfy M m= _1 m