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Pattern Recognition by Matthias Nagel, Matthias Richter, Jürgen Beyerer

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S B w=( m ¯ 1 m ¯ 2 ) ( m ¯ 1 m ¯ 2 ) T w scalar ( 2.234 )

always has the same direction as (m1m2. Therefore, Equation (2.233) can be sim plfied by setting SB w = λ (m1m2) for some unknown scalar λ,

S w 1 λ( m ¯ 1 m ¯ 2 )=λw w= λ 1 λ S w 1 ( m ¯ 1 m ¯ 2 ).( 2.235 )

By virtue of the normalization condition wTSW w = 1 from Equation (2.230), the unknown factor can be cancelled:

w= w w T S w w = S w 1 ( m ¯ 1 m ¯ 2 ) ( m ¯ 1 m ¯ 2 ) T S w 1 T S w S w 1 ( m ¯ 1 m ¯ 2 )

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