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11.3. KRONECKER CANONICAL FORM OF A TWO-PARAMETER PENCIL 219
The degree of ρ 2 is η 2 = 2 and therefore z i (ρ 2 ) can be written as z i (ρ 2 )=z i,0 +
ρ 2 z i,1 + ρ 2 2 z i,2 for i =0, 1. This can be substituted into (11.71). When the notations
(11.69) and (11.70) are used for the matrices B(ρ 2 ) and C(ρ 1 ,ρ 2 ) and the relationships
for the coefficients of the terms in ρ 1 and ρ 2 are worked out again, the following system
of equations occurs:
⎛
M 1,2 ⎜
⎝
z 0,0
z 0,1
z 0,2
z 1,0
z 1,1
z 1,2
⎞
= 0 (11.72)
⎟
⎠
where the dimension of the matrix M 1,2 is ( 1 2 · 3 · 6 · 7) m × (2 · 3) n =63m × 6n.
When the zero block rows of the matrix M 1,2 are discarded, the dimension becomes