The e value is 1 1 0 since sh 1 0 2 ii sc 10

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Unformatted text preview: re multiples of x = 1 0 . The e-value is λ = 1. 1 0 , since Sh 1 0 = 2 (ii) Sc = 10 04 y scale y (1, 4) −→ 1 1 (1, 1) x 1 x Multiples of x1 = λ2 = 4. (iii) P = y 1 0 , x2 = 0 1 , e-values λ1 = 1, 10 00 projection y (1, 1) −→ x x 1 1 1 Multiples of x1 = multiples of x2 = 0 1 1 0 since P x1 = x1 , λ1 = 1 and since P x2 = 0 · x2, λ2 = 0. 3 (iv) Re = 2c2 − 1 2cs 2cs 2s − 1 2 for θ = π/4, 01 10 so c = s = √ 2/2 and Re = . y y 1 −→ θ 1 x 1 x 1 Multiples of x1 = and x2 = 1 −1 1 1 since Re 1 −1 1 1 = 1 −1 1 1 , λ1 = 1 since Re = −1 , λ2 = −1. 4 (v) Ro = s c −s c y y −→ θ x x no e-vector unless θ = π Ro = x1 x2 −1 0 0 −1 e-vector: any vector x = , e-value λ = −1. 5...
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