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10) i = 2, ... 14) where R is a p x p upper triangular matrix and 'P is the product of p Householder transformations. 40 2. 3 it is clear that a transformation QI can be found such that QI X ~ 1 X~2 [ ... 15) : o XN2 ... 1 2 0 Q2QI X =: [ x~p] . o where the first element of u' is X 13 ••. X 1p X23 ... X 2P 0 " : . X~3 ... 16) x~p Continuing this process yields Eq. 14) with 'P = QpQp_1 ... 2. 17) and the p-vector 'II in Eq. 25) where R is upper triangular. 26) where '11 is a p-vector and '12 is an (N - p)-vector.

At. j "I '2 I_ '. t- 0 where it, i2 , ... , in are integers and

40 2. 3 it is clear that a transformation QI can be found such that QI X ~ 1 X~2 [ ... 15) : o XN2 ... 1 2 0 Q2QI X =: [ x~p] . o where the first element of u' is X 13 ••. X 1p X23 ... X 2P 0 " : . X~3 ... 16) x~p Continuing this process yields Eq. 14) with 'P = QpQp_1 ... 2. 17) and the p-vector 'II in Eq. 25) where R is upper triangular. 26) where '11 is a p-vector and '12 is an (N - p)-vector. 19) can be readily solved by back-substitution since R is triangular. 1) [86]. 7. , E{Y} = XO where X is known.

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