ABSTRACT
The n × n matrix Ω-1 of (6.1.16) may be written in the following way: https://www.w3.org/1998/Math/MathML"> Ω ( ρ ) − 1 = ( 1 + ρ 2 ) I − 2 ρ Θ + ρ ( 1 − ρ ) C , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_878_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where https://www.w3.org/1998/Math/MathML"> Θ = 1 2 [ 1 1 0 0 ⋯ 0 0 0 1 0 1 0 ⋯ 0 0 0 0 1 0 1 ⋯ 0 0 0 0 0 1 0 ⋯ 0 0 0 ⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ 0 0 0 0 ⋯ 0 1 0 0 0 0 0 ⋯ 1 0 1 0 0 0 0 ⋯ 0 1 1 ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_879_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> (i.e., https://www.w3.org/1998/Math/MathML"> Θ = [ θ i j ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/inline-math_422_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> with https://www.w3.org/1998/Math/MathML"> θ 11 = θ n n = θ i + 1 , i = θ i , i + 1 = 1 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/inline-math_423_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> θ i j = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/inline-math_424_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> otherwise) and where https://www.w3.org/1998/Math/MathML"> C = [ 1 0 0 ⋯ 0 0 0 0 0 ⋯ 0 0 0 0 0 ⋯ 0 0 ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ 0 0 0 ⋯ 0 0 0 0 0 ⋯ 0 1 ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_880_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> (i.e., https://www.w3.org/1998/Math/MathML"> C = [ c i j ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/inline-math_425_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> with https://www.w3.org/1998/Math/MathML"> c 11 = c n n = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/inline-math_426_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> c i j = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/inline-math_427_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> otherwise).
