Algebraic Solutions of Differential Equations
89
which has the shape
(6.4.0.13)
0
Q(a)
\
*
Q(a+ 1)
",
Q(b
1)
o
/
the ,'s indicating nonzero diagonal terms. If
none
of the offdiagonal
terms vanishes, this matrix obviously has as
image
the subspace
N(<b 1)/N(<a
1) of
N(<=b)/N(<a
1), and hence has onedimen
sional kernel. Conversely, if one of the offdiagonal terms vanishes, then
the matrix (6.4.0.13) is in block form
/
\
(6.4.0.14)
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 Fall '11
 NormanKatz
 Algebraic Solutionsof DifferentialEquations, nonzero diagonal terms, onedimens ional kernel, 6.3.0.13

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