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1. More on the function F. Z = {(z, A) R Sym(Rn
 

Summary: 1. More on the function F.
Let
Z = {(z, A) R Sym(Rn
) : A is invertible and |z| ||A-1
|| < 1}
and note that Z is open. Let
F(z, A) = trace A (1 - z A)-1
for (z, A) G.
Recall that if
inv : GL(Rn
) GL(Rn
)
is inversion then
inv(A)(B) = -A-1
B A-1
whenver A GL(Rn
) and B gl(Rn
).
We have
F(z, A)(1, 0) = trace A (1 - z A)-1

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics